Statistics Questions

According the April 12 2017 Pew Research survey 58 of Americans approve of US missile strikes in Syria in response to reports of the use of chemical weapons by Bashar al Assad s government the Syrian government A sample of 50 Americans are surveyed Let p be the sample proportion of Americans who approve the U S missile strikes 1 What is the population proportion decimal form 2 What is the sample size 3 Can the normal approximation be used with this distribution 4 What is the mean of the sampling proportion 5 What is the standard deviation sampling proportion Round to 4 decimal places 6 What is the probability that no more than 25 Americans of the 50 in the survey approve of the missile strikes What is p What is the z score What is the requested probability P p Round to the nearest hundredth 0 5 7 What is the probability that more than 30 of the 50 Americans in the survey approved of the missile strikes What is p What is the z score Round to the nearest hundredth 0 6 What is the requested probability P p

Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles The results are as follows Lease Length in Months Percent of Leases 13 24 14 8 36 7 25 36 37 48 27 7 49 60 20 5 0 3 More than 60 a Use the midpoint of each class and call the midpoint of the last class 66 5 months for purposes of computing the expected lease term Also find the standard deviation of the distribution Round your answers to two decimal places expected lease term standard deviation 36 93 5 84 X months X b Sketch a graph of the probability distribution for the duration of new auto leases

You wish to test the following claim Ha about the difference of means for two matched samples at a significance level of a 0 001 For the context of this problem one data set represents a pre test and the other data set represents a post test Ho Pa 0 Ha Hd 0 You believe the population of difference scores is normally distributed but you do not know the standard deviation You obtain pre test and post test samples for n 43 subjects The average difference post pre is d 14 2 with a standard deviation of the differences of sd 38 8 a What is the test statistic for this sample test statistic 2 399 o Round to 4 decimal places b What is the p value for this sample Round to 4 decimal places p value 0 0097 X c The p value is less than or equal to a greater than a d This test statistic leads to a decision to reject the null O accept the null O fail to reject the null e As such the final conclusion is that There is sufficient evidence to warrant rejection of the claim that the mean difference of post test from pre test is less than 0 O There is not sufficient evidence to warrant rejection of the claim that the mean difference of post test from pre test is less than 0 The sample data support the claim that the mean difference of post test from pre test is less than 0

Does it pay to ask for a raise A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one According to the survey of the women interviewed 28 asked for a raise and of those women who had asked for a raise 45 received the raise If a woman is selected at random from the survey population of women find the following probabilities Enter your answers decimal places a P woman asked for a raise b P woman received raise given she asked for one c P woman asked for raise and received raise

Each runner has a pair of shoes This table does not have paired data there is no clear relationship between the top and bottom values in any column b Write the hypotheses in symbols O Ho Hdiff new old 0 Ha Hdiff new old 0 O Ho Hdiff new old 0 Ha Hdiff new old 0 Ho Hdiff new old 0 Ha Hdiff new old 0 c Put the list of differences in your calculator and use T Test to find the p value p please round to four decimal places d What is the conclusion of the hypothesis test O Since p 0 05 we support the null hypothesis O Since p 0 05 we reject the null hypothesis and support the alternative O Since p 0 05 we fail to reject the null hypothesis Since p 0 05 we reject the null hypothesis and support the alternative O Since p 0 05 we fail to reject the null hypothesis e What is the final conclusion in everyday language O There is sufficient evidence to support the claim that the wear amounts are different There is sufficient evidence to reject the claim that the wear amounts are different different

Does it pay to ask for a raise A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one According to the survey of the men interviewed 20 hi asked for a raise and 62 of the men who had asked for a raise received the raise If a man is selected at random from the survey population of men find the following probabilities Enter your answers to three decir places a P man asked for a raise b P man received raise given he asked for one c P man asked for raise and received raise

The Orchard Cafe has found that about 6 of the diners who make reservations don t show up If 78 reservations have been made how many diners can be expected to show up Find the standard deviation of this distribution Round your answers to two decimal places H 45 o 2 10

In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even Round your answer to four decimal pla a What is the probability that a subject would guess exactly 18 correct in a series of 36 trials b What is the probability that a subject would guess more than 20 correct in a series of 36 trials

The Orchard Cafe has found that about 6 of the diners who make reservations don t show up If 78 reservations have been made how many diners can be expected to show up Find the standard deviation of this distribution Round your answers to two decimal places 4 68 a 2 10

Consumer Reports rated airlines and found that 81 of the flights involved in the study arrived on time i e within 15 minutes of scheduled arrival time Assuming that the on time arrival rate is representative of the entire commercial airline industry consider a random sample of 206 flights Round your answers to two decimal places What is the expected number that will arrive on time 166 86 What is the standard deviation of this distribution 5 59

Internet tax In 2013 the Gallup Poll asked 1033 U S adults whether they believed that people should pay sales tax on items purchased over the internet Of these 434 said they supported such a tax Does the survey provide convincing evidence that less than 46 of U S adults favor an internet sales tax Use the a 0 10 level of significance and the P value method with the TI 84 Plus calculator Part 1 of 4 a State the null and alternate hypotheses HoP 46 46 This hypothesis test is a left tailed Alternate Answer Ho p 0 46 H p 0 46 This hypothesis test is a left tailed test Part 1 4 Part 2 of 4 test b Compute the P value Round the answer to at least four decimal places

Partial payments are made on the dates indicated Use the United States rule to determine the balance due on the note at the date of maturity The Effective Date is the date the note was written Assume the year is not a leap ye Principal 17 000 Effective Date Sept 12 Partial Payment Amount 7000 6000 Rate 3 6 8 Click the icon to view a table of the number of the day of the year for each date Date Oct 10 Nov 8 The balance due on the note at the date of maturity is Round to the nearest cent as needed Maturity Date Dec 30

TH1123 section OB Fall 202 A certain article indicates that in a sample of 1 000 dog owners 660 said that they take more pictures of their dog than of their significant others or friends and 420 said that they are more likely to complain to their dog than to a friend Suppose that it is reasonable to consider this sample as representative of the population of dog owners LAUSE SALT C Solved The formula used to compute a large sample c a Construct a 90 confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval There is a 90 chance that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls within this interval We are 90 confident that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls within this interval We are 90 confident that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls directly in the middle of this interval We are 90 confident that the mean number of dog owners who take more pictures of their dog than of their significant others or friends falls within this interval There is a 90 chance that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls directly in the middle of this interval b Construct a 95 confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend Enter your answer using interval notation Round your numerical values to three decimal places c Give two reasons why the confidence interval in part b is wider than the interval in part a First the confidence level in part b is higher than Interpret the interval We are 95 confident that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls directly in the middle of this interval There is a 95 chance that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls within this interval There is a 95 chance that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls directly in the middle of this interval We are 95 confident that the mean number of dog owners who are more likely to complain to their dog than to a friend falls within this interval We are 95 confident that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls within this interval the confidence level in part a so the z critical value for part b is larger than the z critical value for part a Second the

In a survey of 800 college students in the United States 568 indicated that they believe that a student or faculty member on campus who uses language considered racist sexist homophobic or offensive should be subject to disciplinary action USE SALT MY NOTES Assuming that the sample is representative of college students in the United States construct a 95 confidence interval for the proportion of college students who have this belief Enter your answer using interval notation Round your numerical values to three decimal places PRACTICE ANOTHER Interpret the interval We are 95 confident that the true proportion of U S college students who believe that a student or faculty member on campus who uses language considered racist sexist homophobic or offensive should be subject to disciplinary action falls directly in the middle of this interval We are 95 confident that the true proportion of U S college students who believe that a student or faculty member on campus who uses language considered racist sexist homophobic or offensive should be subject to disciplinary action falls within this interval There is a 95 chance that the true proportion of U S college students who believe that a student or faculty member on campus who uses language considered racist sexist homophobic or offensive should be subject to disciplinary action falls within this interval There is a 95 chance that the true proportion of U S college students who believe that a student or faculty member on campus who uses language considered racist sexist homophobic or offensive should be subject to disciplinary action falls directly in the middle of this interval Read It We are 95 confident that the mean number of U S college students who believe that a student or faculty member on campus who uses language considered racist sexist homophobic or offensive should be subject to disciplinary action falls within this interval Need Help Master It

An article included data from a survey of a random sample of adults living in the United States Of the 1 300 people who participated in the survey 700 responded they believe that global climate change is a major threat to the well being of the United States USE SALT O MY NOTES Use the five step process for estimation problems EMC3 to construct a 95 confidence interval for the proportion of adults in the United States who believe that global climate change is a major threat to the well being of the United States Hint See Example 9 4 Enter your answer using interval notation Round your numerical values to three decimal places PRACTICE ANOTHER Interpret the interval We are 95 confident that the true proportion of all adults in the United States who believe that global climate change is a major threat to the well being of the United States is directly in the middle of this confidence interval We are 95 confident that the mean number of all adults in the United States who believe that global climate change is a major threat to the well being of the United States is within this confidence interval There is a 95 chance that the mean number of all adults in the United States who believe that global climate change is a major threat to the well being of the United States is directly in the middle of this confidence interval Need Help We are 95 confident that the true proportion of all adults in the United States who believe that global climate change is a major threat to the well being of the United States is within this confidence interval There is a 95 chance that the true proportion of all adults in the United States who believe that global climate change is a major threat to the well being of the United States is directly in the middle of this confidence interval Read It

What statistic did you use sample proportion Opopulation proportion An article about the relative priorities of protecting the environment and the economy in America summarized a survey of 1 700 adult U S citizens When asked if they expect to feel the effects of climate change in their lifetime 1 037 of the survey participants responded yes The article states that participants were selected to be representative of all adult U S citizens a Estimate the proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime b Use the sample data to estimate the standard error of p Round your answer to three decimal places MY NOTES c Calculate the margin of error associated with the estimate in Part a Hint See Example 9 3 Round your answer to three decimal places PRACTICE ANOTHER Interpret the margin of error in the context of this problem It is unlikely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by less than the calculated value It is likely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by the calculated value It is impossible that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by more than the calculated value It is impossible that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by less than the calculated value It is unlikely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by

Data from a representative sample were used to estimate that 33 of all computer users in a recent year had tried to get on a Wi Fi network that was not their own in order to save money You decide to conduct a survey to estimate this proportion for the current year What is the required sample size if you want to estimate this proportion with a margin of error of 0 04 USE SALT Calculate the required sample size first using 0 33 as a preliminary estimate of p Round your answer up to the nearest integer Calculate the required sample size using the conservative value of 0 5 Round your answer up to the nearest integer How do the two sample sizes compare The sample size computed using the preliminary estimate is smaller than the sample size computed using the conservative value What sample size would you recommend for this study Round your sample size up to the nearest integer The sample size of error no greater than 0 04 if p Need Help MY NOTES Read It PRACTICE ANOTHER should be used for this study because it will guarantee a margin of error of no greater than 0 04 The other sample size computed will only guarantee a margin of or if p

An article about the relative priorities of protecting the environment and the economy in America summarized a survey of 1 600 adult U S citizens When asked whether protecting the environment or protecting jobs should have a higher priority 832 of the survey participants chose protecting the environment The article states that participants were selected to be representative of all adult U S citizens a Estimate the proportion of adult U S citizens who think that protecting the environment should be a higher priority than protecting jobs What statistic did you use What statistic did you use O sample proportion population proportion MY NOTES b Use the sample data to estimate the standard error of p c Calculate the margin of error associated with the estimate in Part a Round your answer to three decimal places PRACTICE ANOTHER Interpret the margin of error in the context of this problem It is impossible that the estimated proportion of adult U S citizens who think that protecting the environment should be a higher priority than protecting jobs differs from the true population proportion by less than the calculated value It is unlikely that the estimated proportion of adult U S citizens who think that protecting the environment should be a higher priority than protecting jobs differs from the true population proportion by more than the calculated value OIt is impossible that the estimated proportion of adult U S citizens who think that protecting the environment should be a higher priority than protecting jobs differs from the true population proportion by more than the calculated value It is likely that the estimated proportion of adult U S citizens who think that protecting the environment should be a higher priority than protecting jobs differs from the true population proportion by the calculated value It is unlikely that the estimated proportion of adult U S citizens who think that protecting the environment should be a higher priority than protecting jobs differs from the true population proportion by less than the calculated value

No less than 8 MY NOTES The U S Census Bureau reported that in 2019 the proportion of adult Americans ages 25 and older who have a bachelor s degree or higher is 0 36 t Consider the population of all adult Americans ages 25 and over in 2019 and define p to be the proportion of people in a random sample from this population who have a bachelor s degree or higher a Would p based on a random sample of only 10 people from this population have a sampling distribution that is approximately normal Explain why or why not approximately normally distributed because np is the sampling distribution of p based on a random sample of size 10 residents would not be 10 b What are the mean and standard deviation of the sampling distribution of p if the sample size is 600 Round your standard deviation to four decimal places mean standard deviation PRACTICE ANOTHER c Suppose that the sample size is n 300 rather than n 600 What are the values for the mean and standard deviation when n 300 Round your standard deviation to four decimal places mean standard deviation Does the change in sample size affect the mean and standard deviation of the sampling distribution of p If not explain why not Select all that apply When the sample size decreases the mean increases When the sample size decreases the mean decreases When the sample size decreases the mean stays the same The sampling distribution is always centered at the population mean regardless of sample size When the sample size decreases the standard deviation increases When the sample size decreases the standard deviation decreases When the sample size decreases the standard deviation stays the same The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution regardless of sample size

Submit Answer 9 1 Points In spite of the potential safety hazards some people would like to have an Internet connection in their car A preliminary survey of adult Americans has estimated this proportion to be somewhere around 0 20 Use the given preliminary estimate to determine the sample size required to estimate this proportion with a margin of error of 0 02 Round your answer up to the nearest integer DETAILS PECKSTAT3 9 4 501 XP MI S USE SALT You may need to use the appropriate table in the appendix to answer this question MY NOTE

Forensic evidence such as DNA analysis and fingerprints is often introduced as part of the evidence presented in criminal trials A paper describes a study to learn about how potential jurors view forensic evidence Each person in a sample of 153 adult Americans was asked if they agreed with the following statement If forensic evidence suggests a defendant is guilty this should be enough convict even if other evidence e g eyewitness testimony alibi suggest otherwise Fifty nine responded that they agreed either strongly agreed or somewhat agreed with this statement Suppos that it is reasonable to regard this sample as a random sample from the population of potential jurors and that you are interested in learning about the proportion of all potential jurors who agree with the given statement The following table is similar to the table that appears in Examples 8 4 and 8 5 and is meant to summarize what you know about the sampling distribution of p in the situation just described The What You Know information has been provided Complete the table by filling in the How You Know It column What You Know The sampling distribution of p is centered at the actual but unknown value of the population proportion An estimate of the standard deviation of p which describes how much the p values spread out around the population is 0 0394 H P P p p H p p OH p 59 153 Hp 59 153 59 153 1 59 153 153 1 153 153 1 59 153 59 153 153 59 1 59 153 59 153 59 MY NOTES How You Know It

The formula used to calculate a large sample confidence interval for p is P 1 P pa z critical value n What is the appropriate z critical value for each of the following confidence levels Round your answers to two decimal places a 95 b 96 c 83 Submit Answer LAUSE SALT

One thousand randomly selected adult Americans participated in a survey When asked Do you think it is sometimes justified to lie or do you think lying is never justified 55 responded that lying was never justified When asked about lying to avoid hurting someone s feelings 670 responded that this was often or sometimes OK USE SALT a Construct a 90 confidence interval for the proportion of adult Americans who think lying is never justified Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval We are 90 confident that the true proportion of adult Americans who think lying is never justified falls directly in the middle of this interval There is a 90 chance that the true proportion of adult Americans who think lying is never justified falls within this interval c We are 90 confident that the mean number of adult Americans who think lying is never justified falls within this interval There is a 90 chance that the true proportion of adult Americans who think lying is never justified falls directly in the middle of this interval We are 90 confident that the true proportion of adult Americans who think lying is never justified falls within this interval MY NOTES b Construct a 90 confidence interval for the proportion of adult Americans who think that it is often or sometimes OK to lie to avoid hurting someone s feelings Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval We are 90 confident that the true proportion of adult Americans who think that it is often or sometimes OK to lie to avoid hurting someone s feelings falls directly in the middle of this interval There is a 90 chance that the true proportion of adult Americans who think that it is often or sometimes OK to lie to avoid hurting someone s feelings falls within this interval We are 90 confident that the true proportion of adult Americans who think that it is often or sometimes OK to lie to avoid hurting someone s feelings falls within this interval There is a 90 chance that the true proportion of adult Americans who think that it is often or sometimes OK to lie to avoid hurting someone s feelings falls directly in the middle of this interval We are 90 confident that the mean number of adult Americans who think that it is often or sometimes OK to lie to avoid hurting someone s feelings falls within this interval Using the confidence intervals from parts a and b comment on the apparent inconsistency in the responses 500 of adult Americans would say that lying is never justified The confidence interval in part b

A report on consumer financial literacy summarized data from a representative sample of 2 001 adult Americans When asked if they typically carry credit card debt from month to month 844 of these people responded yes a Use the given information to estimate the proportion of adult Americans who carry credit card debt from month to month Round your answer to three decimal places b Verify that the conditions needed in order for the margin of error formula to be appropriate are met The condition that the sample is a random sample from the population of interest or the sample is selected in a way that should result in a representative sample is met the sample size is large is met 0 c Calculate the margin of error Round your answer to three decimal places MY NOTES The condition that d Interpret the margin of error in the context of this problem It is unlikely that the estimated proportion of adult Americans who carry credit card debt from month to month differs from the true population proportion by less than the value calculated in part c It is likely that the estimated proportion of adult Americans who carry credit card debt from month to month differs from the true population proportion by the value calculated in part c It is impossible that the estimated proportion of adult Americans who carry credit card debt from month to month differs from the true population proportion by more than the value calculated in part c OIt is unlikely that the estimated proportion of adult Americans who carry credit card debt from month to month differs from the true population proportion by more than the value calculated in part c It is impossible that the estimated proportion of adult Americans who carry credit card debt from month to month differs from the true population proportion by less than the value calculated in part c

Suppose that 925 smokers each received a nicotine patch which delivers nicotine to the bloodstream at a much slower rate than cigarettes do Dosage was decreased to 0 over a 12 week period Of these 925 people 245 were still not smoking 6 months after treatment Assume this sample is representative of all smokers MY NOTES a Use the given information to estimate the proportion of all smokers who when given this treatment would refrain from smoking for at least 6 months Round your answer to three decimal places b Verify that the conditions needed in order for the margin of error formula to be appropriate are met The condition that the sample is a random sample from the population of interest or the sample is selected in a way that should result in a representative sample is met condition that the sample size is large is met c Calculate the margin of error Round your answer to three decimal places B The d Interpret the margin of error in the context of this problem O It is impossible that the estimated proportion of smokers who when given this treatment would refrain from smoking for at least six months differs from the true population proportion by less than the value calculated in part c It is unlikely that the estimated proportion of smokers who when given this treatment would refrain from smoking for at least six months differs from the true population proportion by more than the value calculated in part c It is unlikely that the estimated proportion of smokers who when given this treatment would refrain from smoking for at least six months differs from the true population proportion by less than the value calculated in part c It is impossible that the estimated proportion of smokers who when given this treatment would refrain from smoking for at least six months differs from the true population proportion by more than the value calculated in part c It is likely that the estimated proportion of smokers who when given this treatment would refrain from smoking for at least six months differs from the true population proportion by the value calculated in part c

Three different statistics are being considered for estimating a population characteristic The sampling distributions of the three statistics are shown in the following illustration Statistic II Statistic III Statistic I Submit Answer Value of population characteristic Statistic II Which of these statistics are unbiased estimators of the population characteristic Select all that apply Statistic I Statistic III M

PRACTICE ANOTHER An article summarizes results from a survey of 420 participants The article reported that 71 of the 420 survey participants said that they had made up an excuse not to attend an online meeting just because they didn t feel like attending the most popular excuse was internet problems If p 0 71 is used as an estimate of the proportion of working adults who have made up an excuse not to attend an online meeting is it likely that this estimate is within 0 05 of the actual population proportion Use what you know about the sampling distribution of p to support your answer Round your answer to four decimal places We know the sampling distribution of p will be centered at the Select distribution is approximately normal So we can and the standard deviation of this distribution can be estimated as 8 say our value of p is likely to be within 0 05 of the actual value because of the following fact The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center and two standard deviations is less than 0 05 The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center but two standard deviations is greater than 0 05 The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center and our standard deviation is less than 0 05 We cannot make use of the Empirical Rule since our sampling distribution isn t mound shaped and symmetric O The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center but our standard deviation is greater than 0 05 Need Help Read It In addition the sampling

A news article estimated that only 4 of those age 65 and older who prefer to watch the news rather than to read or listen watch the news online This estimate was based on a survey of a large sample of adult Americans Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news and suppose that for this population the actual proportion who prefer to watch online is 0 04 standard deviation Content a A random sample of n 100 people will be selected from this population and p the proportion of people who prefer to watch online will be calculated What are the mean and standard deviation of the sampling distribution of p Round your standard deviation to four decimal places mean b Is the sampling distribution of p approximately normal for random samples of size n 100 Explain The sampling distribution of p is approximately normal because np is less than 10 The sampling distribution of p is approximately normal because np is at least 10 The sampling distribution of p is not approximately normal because np is less than 10 The sampling distribution of p is not approximately normal because np is at least 10 O The sampling distribution of p is not approximately normal because n 1 p is less than 10 mean standard deviation c Suppose that the sample size is n 400 rather than n 100 What are the values for the mean and standard deviation when n 400 Round your standard deviation to four decimal places W Chapter 8 Homework MATH1123 section OB Fall 2023 WebAssign Does the change in sample size affect the mean and standard deviation of the sampling distribution of p If not explain why not Select all that apply When the sample size increases the mean increases When the sample size increases the mean decreases When the sample size increases the mean stays the same The sampling distribution is always centered at the population mean regardless of sample size When the sample size increases the standard deviation increases When the sample size increases the standard deviation decreases When the sample size increases the standard deviation stays the same The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution regardless of sample size d Is the sampling distribution of p approximately normal for random samples of size n 400 Explain TO The sampling distribution of p is approximately normal because np and n 1 p are both at least 10 O The sampling distribution of p is approximately normal because np and n 1 p are both less than 10 approximately normal because np and n 1 p are both at least 10

MY NOTES An article discussing a rise in the proportion of Americans with tattoos over a seven year period describes a survey of 1 009 adult Americans Suppose that it is reasonable to regard this sample as a random sample from the population of adult Americans Of the survey participants 289 reported that they had at least one tattoo a Suppose you are interested in learning about the value of p the proportion of all adult Americans who have at least one tattoo This proportion can be estimated using the sample proportion p What is the value of p for this sample Round your answer to four decimal places pa PRACTICE ANOTHER b Based on what you know about the sampling distribution of p is it reasonable to think that this estimate is within 0 05 of the actual value of the population proportion Explain why or why not Hint See Example 8 4 Round your answer to four decimal places Need Help We know the sampling distribution of p will be centered at the Select sampling distribution is approximately normal the following fact The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center and our standard deviation is less than 0 05 We cannot make use of the Empirical Rule since our sampling distribution isn t mound shaped and symmetric The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center but two standard deviations is greater than 0 05 The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center and two standard deviations is less than 0 05 The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center but our standard deviation is greater than 0 05 Read It and the standard deviation of this distribution can be estimated as So we can In addition the B say our value of p is likely to be within 0 05 of the actual value because of

article The Average American Is in Credit Card Debt No Matter the Economy reported that only 35 of credit card users pay off their bill every month Suppose that the reported percentage was based on a random sample of 2 000 credit card users You are interested in learning about the value of p the proportion of all credit card users who pay off their bill every month The following table is similar to the table that appears in Examples 8 4 and 8 5 and is meant to summarize what you know about the sampling distribution of p in the situation just described The What You Know information has been provided Complete the table by filling in the How You Know It column What You Know The sampling distribution of p is centered at the actual but unknown value of the population proportion An estimate of the standard deviation of p which describes how much the p values spread out around the population proportion p is 0 011 p Hp p p X P Hp P p 0 35 1 0 35 2 000 Hp V H V 0 35 10 35 2 000 0 35 1 0 35 2 000 0 35 1 0 35 2 000 0 35 1 0 35 2 000 How You Know It largo A ANOTHER and n is not too close to 0 or 1

For which of the following sample sizes would the sampling distribution of p be approximately normal when p 0 3 Select all that apply n 10 n 25 n 50 n 100 For which of the following sample sizes would the sampling distribution of p be approximately normal when p 0 7 Select all that apply n 10 n 25 n 50 n 100 A For which of the following sample sizes would the sampling distribution of p be approximately normal when p 0 58 Select all that apply n 10 n 25 n 50 n 100

A random sample is to be selected from a population For which of the following sample sizes would the sampling distribution of p be approximately normal if p 0 60 Select all that apply n 10 n 20 n 30 n 50 n 100 R n 200 For which of the following sample sizes would the sampling distribution of p be approximately normal if p 0 3 Select all that apply n 10 n 20 n 30 n 50 n 100 n 200 Watch It

grams and a standard deviation of 450 grams Use a 0 01 significance level to test the claim that the standard deviation of birth weights of American babies is equal to 600 grams Ho o 600 H o 600 Claim Test Statistics

6 A sample of 50 earthquake depths has a mean of 10 km Use a 0 01 significance level to test the claim of a seismologist that these earthquakes are from a population that has a mean depth less than 10 km Assume that the population standard deviation is known to be 5 km Ho M 5 H M 5 Claim Test Statistics

4 In a presidential election 300 out of 600 voters surveyed said that they voted for the candidate who won Use a 0 10 significance level to test the claim that the percentage of all voters are believed to have voted for the winning candidate is greater than 45 Ho p 0 45 Ha P 0 45 claim Test Statistics

5 When 40 people used the Weight Watchers diet for one year the mean weight loss was 3 pounds and the standard deviation was 5 pounds Use a 0 01 significance level to test the claim that the mean weight loss is greater than 0 Ho M 0 Ha M 0 claim Test Statistics

3 Listed below are the ages of randomly selected race car drivers Construct a 99 confidence interval estimate of the mean age of all race car drivers 30 31 33 34 45 29 38 39 33 21 27 45 56 39 25

2 You have been hired by a college foundation to conduct a survey of graduates If you want to estimate the percentage of graduates who have made a donation to the college after graduation then how many graduates must you survey if you want 90 confidence that your percentage has a margin of error of Three percentage points

6 The disease status and exposure of a small population is summarized in the given table below An individual is randomly selected from this population Define A to be the event that the selected individual has been exposed and define event B to be the event that the selected individual has the disease Find P A B Exposure No Exposure Answer Disease 56 24 Previous Answer 0 7 No Disease 384 668

7 The disease status and exposure of a small population is summarized in the given table below An individual is randomly selected from this population Define A to be the event that the selected individual has been exposed and define event B to be the event that the selected individual has the disease Find the probability that the individual has the disease given they have not been exposed i e find P BIA Exposure No Exposure Disease Answer 64 18 No Disease Previous Answer none 404 Round your answer to the nearest thousandths 712

1 In a Gallup poll of 1000 adults were asked if they consume alcohol beverages and 60 of them said that they did Construct a 95 confidence interval of the proportion of all adults who consume alcohol beverages

You wish to test the following claim Ha at a significance level of a 0 001 d denotes the mean of the difference between pre test and post test scores Ho Pd 0 Ha Pd 0 You believe the population of difference scores is normally distributed but you do not know the standard deviation You obtain the following sample of data post test pre test 51 5 41 4 61 8 74 5 61 5 57 9 51 8 48 9 49 9 45 9 61 1 50 5 54 9 50 5 54 3 74 1 68 4 59 9 55 5 67 5 60 2 54 2 65 2 48 9 71 4 42 2 60 7 45 8 40 83 1 86 7 58 1 Make sure to choose the appropriate column for Sample 1 and 2 so that you are estimating the improved post test score pre test post test 2 1 a What is the test statistic for this sample test statistic Round to 3 decimal places b What is the p value for this sample Round to 4 decimal places p value A c The p value is O less than or equal to a

Ha Hdiff before after 0 c Put the list of differences in your calculator and use T Test to find the p value p please round to four decimal places d What is the conclusion of the hypothesis test O Since p 0 05 we fail to reject the null hypothesis OS nce p 0 05 we reject the null hypothesis and support the alternative O Since p 0 05 we support the null hypothesis O Since p 0 05 we fail to reject the null hypothesis O Since p 0 05 we reject the null hypothesis and support the alternative e What is the final conclusion in everyday language O There is sufficient evidence to support the claim that the diet changes the average blood sugar level O There is sufficient evidence to reject the claim that the diet changes the average blood sugar level O There is not sufficient evidence to reject the claim that the diet changes the average blood sugar level O There is not sufficient evidence to support the claim that the diet changes the average blood sugar level

5 Assume each outcome is equally likely in the sample space S provided below Find P AB S 1 2 3 4 5 6 7 8 A 2 4 5 6 B 1 2 3 5 Do not round your answer Answer

Question 7 of 7 7 Suppose P A 25 P B 0 30 and P AB 0 15 Find P AUB Answer

Question 5 3 Assuming each outcome is equally likely in the sample space find P AUB FOB Answer

A company estimates that 0 8 of their products will fail after the original warranty period but within 2 years of the purchase with a replacement cost of 100 If they offer a 2 year extended warranty for 8 what is the company s expected value of each warranty sold

Find the standard deviation for the random variable X 1 1 7 10 14 P X x 0 16 0 17 0 24 0 17 0 26 X O 4 5069009307949 O4 9444663008256 O 5 5343563311373 O 5 3971795412048 24127569109

Find the expected value for the random variable X 3 1 3 9 12 P X x 0 22 0 14 0 23 0 2 0 21 X O 3 8 2 69 O4 35 01 97 O 4 49 O 5 15

A sample of size n 10 is drawn from a population The data is shown below 102 6 98 3 102 6 86 4 87 6 102 6 82 2 78 8 70 8 61 9 What is the range of this data set range What is the standard deviation of this data set Remember it is a sample Please report the answer with appropriate rounding reporting 2 more decimal places than the original data Please please please do not calculate the value by hand