Statistics Questions

Researchers studied the mean egg length in millimeters for a bird population After taking a random sample tempts of eggs they obtained a 95 confidence interval of 45 60 What is the value of the sample mean Choose the correct answer below COL OA 15 0 mm OB 7 5 mm OC 52 5 mm OD Somewhere between 45mm and 60mm but the exact value cannot be determined without more information tempts tempts tempts tempts

4 Each bag of different colored jelly beans is supposed to have 30 blue jelly beans Ramon believes there are actually a greater proportion of blue jelly beans He randomly selects 25 bags of jelly beans and finds the proportion of blue jelly beans to be 36 He uses a significance level of a 0 1 and calculates a p value of 0 256 What null and alternative hypothesis did Ramon use for the test and what conclusion can he make 1 F OH p 0 36 H p 0 36 Ramon fails to reject the null hypothesis because the p value is greater than the significance OH p 0 3 H p 0 3 Ramon fails to reject the null hypothesis because the p value is greater than the significance O H p 0 3 H p 0 3 Ramon rejects the null hypothesis because the p value is greater than the significance level

Are you smarter than a second grader A random sample of 62 second graders in a certain school district are given a standardized mathematics skills test The sample mean score is x 54 Assume the standard deviation of test scores is o 17 The nationwide average score on this test is 50 The school superintendent wants to know whether the second graders in her school district have greater math skills than the nationwide average Use the a 0 01 level of significance and the P value method with the TI 84 calculator Part 0 4 Part 1 of 4 State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test 0 0 O O 0 0

A 99 confidence interval for the mean surgery time for this procedure is 132 8 143 4 Part 1 2 Part 2 of 2 X S b If a 90 confidence interval were constructed with these data would it be wider or narrower than the interval constructed in part a Explain The new confidence interval would be Choose one than the interval constructed in part a Es

If a Type II error is made what conclusion will be drawn regarding the mean breaking strength The conclusion will be that the mean breaking strength is less than 50 Part 2 3 Part 3 of 3 X This test uses a one tailed alternative hypothesis Explain why a one tailed hypothesis is more appropriate than a two tailed hypothesis in this situation With a one tailed hypothesis we can conclude that the mean breaking strength is Choose one two tailed hypothesis we will not know whether the mean breaking strength is Choose one 50 With a 50 X

A 98 confidence interval for the proportion of people who performed volunteer work in the past year is Part 2 3 Part 3 of 3 X p c A sociologist states that 45 of Americans perform volunteer work in a given year Does the confidence interval contradict this statement Explain The confidence interval Choose one contradict the claim because 0 45 Choose one contained in the confidence interval Espa

A concerned group of citizens wanted to determine whether the proportion of armed robberies in the state of Texas was different in 2011 than in 2010 Research shows that of the 113 231 violent crimes in Texas in 2010 7 622 of them were armed robberies In 2011 7 439 of the 104 873 violent crimes were in the armed robery category Test at the 0 01 significance level Preliminary a Is it safe to assume that n2010 5 of all violent crimes during 2010 and 72011 5 of all violent crimes during 2011 Yes No b Verify np 1 P 10 Round your answer to one decimal place n2010P 1 P n2011 1 P Test the claim a Determine the null and alternative hypotheses Ho P2010 P2011 Ha P2010 P2011 b Determine the test statistic Round to two decimal places z c Find the p value Round to four decimals p value

Part 1 of 2 a An article in a medical journal suggested that approximately 5 of such operations result in complications Using this estimate what sample size is needed so that the confidence interval will have a margin of error of 0 05 A sample of 182 operations is needed to obtain a 99 8 confidence interval with a margin of error of 0 05 using the estimate 0 05 for p Part 1 2 Part 2 of 2 b Estimate the sample size needed if no estimate of p is available A sample of operations is needed to obtain a 99 8 confidence interval with a margin of error of 0 05 when no estimate of p is available X

Testing testing An instructor believes that the mean time that students will spend on the take home test is 8 hours A test is made of H 8 versus H 8 The null hypothesis is rejected State an appropriate conclusion There Choose one enough evidence to conclude that the mean time spent is Choose one 8 hours 13 X

b Should this confidence interval be used to estimate the mean weight of all one year old babies in the United States Explain The confidence interval Choose one be used to estimate the mean weight of all one year old babies in the United States Part 2 3 Part 3 of 3 X 3 c Based on the confidence interval constructed in part a is it likely that the mean weight of all one year old boys is less than 28 pounds It Choose one likely that the mean weight of all one year old boys is less than 28 pounds is is not

a Construct a 90 confidence interval for the mean weight or all one year old baby boys in the United States Round the answer to at least one decimal place A 90 confidence interval for the mean weight in pounds of all one year old baby boys in the United States is 25 26 Part 1 3 Part 2 of 3 X b Should this confidence interval be used to estimate the mean weight of all one year old babies in the United States Explain The confidence interval Choose one be used to estimate the mean weight of all one year old babies in the United States should should not

3 A bus company is doing research to determine if it can save money by switching from gasoline powered buses to electric powered buses The company randomly selects records of gasoline usage from 30 days and calculates that the buses use a mean 22 gallons of gas each day with a standard deviation of 1 8 gallons The gas station the buses use charges 2 95 for a gallon of gas The company also knows it would cost 62 to charge the buses enough to be able to run for one day Use a 95 confidence interval to recommend a strategic decision for the bus company

Part 0 5 Part 1 of 5 3 4 Ho 5 a State the appropriate null and alternate hypotheses tast 6 7 Confidence in banks A poll conducted asked a random sample of 1358 adults in the United States how much confidence they had in banks and other financial institutions A total of 149 adults said that they had a great deal of confidence An economist claims that less than 13 of U S adults have a great deal of confidence in banks Can you conclude that the economist s claim is true Use both a 0 10 and a 0 01 levels of significance and the P value method with the TI 84 Plus calculator 0 0 000 0 040 P Y 8 3 9 10 11 612 13 Bepens 17 de

Smartphones A poll agency reports that 24 of teenagers aged 12 17 own smartphones A random sample of 75 teenagers is drawn Round your answers to at least four decimal places as needed Part 0 6 Part 1 of 6 a Find the mean P The mean is 0 24 P Part 1 6 Part 2 of 6 X b Find the standard deviation 0 P Ella Esp

Part 0 5 Part 1 of 5 a State the appropriate null and alternate hypotheses Big babies The National Health Statistics Reports described a study in which a sample of 345 one year old baby boys were weighed Their mean weight was 25 7 pounds with standard deviation 5 3 pounds A pediatrician claims that the mean weight of one year old boys is greater than 25 pounds Do the data provide convincing evidence that the pediatrician s claim is true Use the a 0 05 level of significance and the P value method with the TI 84 Plus calculator Ho H This hypothesis test is a Choose one test X O 0 0 3 10 3 11 12 13

Part 0 2 5 Part 1 of 2 6 8 9 10 11 Surgical complications A medical researcher wants to construct a 99 8 confidence interval for the proportion of knee replacement surgeries that result in complications 12 A sample of operations is needed to obtain a 99 8 confidence interval with a margin of error of 0 05 using the estimate 0 05 for p 13 a An article in a medical journal suggested that approximately 5 of such operations result in complications Using this estimate what sample size is needed so that the confidence interval will have a margin of error of 0 05 X Espar d

Part 0 2 9 Part 1 of 2 10 11 Hip surgery In a sample of 129 hip surgeries of a certain type the average surgery time was 138 1 minutes with a standard deviation of 23 3 minutes 12 a Construct a 99 confidence interval for the mean surgery time for this procedure Round your answers to one decimal place A 99 confidence interval for the mean surgery time for this procedure is 13

Part 0 5 7 Part 1 of 5 8 9 X 10 11 SAT scores Assume that in a given year the mean mathematics SAT score was 467 and the standard deviation was 105 A sample of 59 scores is chosen Use Excel a What is the probability that the sample mean score is less than 455 Round the answer to at least four decimal places The probability that the sample mean score is less than 455 is 12 13

A research study was conducted about gender differences in sexting the sending of sexually explicit messages or images by cell phone A researcher believes that the proportion of girls sexting is less than the proportion of boys sexting and decides to collect data in the spring of 2010 among a random sample of middle and high school students in a large school district in the southern United States The researcher finds 156 out of 2 169 girls are sexting and 183 out of 2 231 boys are sexting Is there enough evidence to support the researcher s belief that the proportion of girls sexting is less than the proportion of boys sexting Test at the 0 01 level of significance Preliminary a Is it safe to assume that ngirls 5 of all girls in middle and high school students in a large school district in the southern United States and nboys 5 of all boys in middle and high school students in a large school district in the southern United States No Yes b Verify np 1 P 10 Round your answer to one decimal place ngirlsp 1 P nboysp 1 P Test the claim a Determine the null and alternative hypotheses Ho Pgirls Pboys Ha Pgirls Pboys b The hypothesis test is Select an answer c Determine the test statistic Round to two decimal places d Find the p value Round to four decimal places p value

Part 0 3 5 Part 1 of 3 6 7 8 9 10 11 12 Babies According to a recent report a sample of 300 one year old baby boys in the United States had a mean weight of 25 5 pounds Assume the population standard deviation is o 5 2 pounds 13 a Construct a 90 confidence interval for the mean weight of all one year old baby boys in the United States Round the answer to at least one decimal place A 90 confidence interval for the mean weight in pounds of all one year old baby boys in the United States is 0 0

Part 0 6 Part 1 of 6 a Find the mean P 5 The mean ile 6 7 8 9 10 Smartphones A poll agency reports that 24 of teenagers aged 12 17 own smartphones A random sample of 75 teenagers is drawn Round your answers to at least four decimal places as needed 11 12 13

A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie Among the 1500 responders 13 chose Chocolate pie the mangin Of error was given as t percentage points Given Specific sample data which confidence interval is wider 90 confidence interval of the 80

Correct Answer The 40th Part 3 5 Part 4 of 5 percentile of the sample mean is 2 20 d Would it be unusual for the sample mean to be less than 2 Round your answer to at least four decimal places unusual because the probability of the sample mean being less than 2 is It Choose one

Let Y represent the profit or loss for a certain company X years after 1980 Based on the data shown below a statistician calculates a linear model Y 2 16X 2 91 X 3 4 5 y y 9 08 6 16 66 7 18 32 11 94 12 9 8 21 88 9 23 44 10 22 7 11 25 36 14 15 12 27 02 13 31 78 16 17 32 64 36 7 36 96 40 42 Use the model to estimate the profit in 1985

Correct Answer The probability that the sample mean number of TV sets is between 2 5 and 3 is 0 0390 Part 2 5 Part 3 of 5 c Find the 40th percentile of the sample mean Round the answer to at least two decimal places The 40th percentile of the sample mean is

c Find the probability that the proportion of individuals in the sample of 83 who have high blood pressure is between 0 20 and 0 32 Round the answer to at least four decimal places The probability that the proportion of individuals in the sample of 83 who have high blood pressure is between 0 20 and 0 32 is 0 6311 Part 3 5 Part 4 of 5 d Find the probability that less than 21 of the people in the sample of 83 have high blood pressure Round the answer to at least four decimal places The probability that less than 21 of the people in the sample of 83 have high blood pressure is 8 M ve

Send data to Excel Part 1 of 2 a Construct a 95 confidence interval for the mean weight Round the answers to at least three decimal places A 95 confidence interval for the mean weight is 14 0555 u 14 1283 Part 1 2 Part 2 of 2 b The quality control manager is concerned that the mean weight is actually less than 14 ounces Based on the confidence interval is there a reason to be concerned Explain The quality control manager should Choose one concerned that the mean weight is actually less than 14 ounces X S

A musicologist wishes to determine if playing classical music makes cows produce more milk Suppose previous research has established that the average daily milk production for cows is 22 liters The researcher therefore decides to test the hypotheses Ho 22 vs H 22 where average milk production when listening to classical music To do so the researcher has played classical music recordings to 10 000 cows at randomly selected dairy farms The mean production for these cows is X 22 006 and the p value for the significance test is 0 0002 What statement below best describes the appropriate conclusion to draw from this study There is not enough evidence to suggest that playing classical music increases cow s milk productivity Although the researcher has obtained a statistically significant result it appears to have little practical significance Since the P value is greater than the reciprocal of the sample size this is not a significant result

A 99 8 confidence interval for the mean number of personal computers is 2 703 Part 2 of 4 b If the sample size were 165 rather than 195 would the margin of error be larger or smaller than the result in part a Explain The margin of error would be larger in the sample size will increase since a decrease the standard error Part 2 4 2 937 Part 3 of 4 c If the confidence levels were 99 9 rather than 99 8 would the margin of error be larger or smaller than the result in part a Explain The margin of error would be Choose one since Choose one in the confidence level will Choose one the critical value

Part 2 of 3 b Construct a 98 confidence interval for the proportion of all customers who experienced an interruption Round the answers to at least three decimal places A 98 confidence interval for the proportion of all customers who experienced an interruption is 0 102 p 0 179 Part 2 3 Part 3 of 3 c The company s quality control manager claims that no less than 10 of its customers experienced an interruption during the previous month Does the confidence interval contradict this claim Explain because all of the values in the confidence interval are Choose one 0 1 Choose one 15 01

Internet tax 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 0 5 Part 1 of 5 State the appropriate null and alternate hypotheses Ho H 0 0 0 0 0 P 8 20

Correct Answer Yes the sample size is small but we can see that the sample seems to come from a population with an approximately normal distribution Part 1 6 b Perform a hypothesis test to determine whether you can conclude that the mean score in 2019 differs from the mean score in 2018 Assume the population standard deviation is a 118 Use the a 0 10 level of significance and the P value method with the TI 84 Plus calculator State the null and alternate hypotheses H H 42 H 42 X D O D O 0 0 Espa ol 8E 20

IQ Scores on a certain IQ test are known to have a mean of 100 A random sample of 41 students attend a series of coaching classes before taking the test Let u be the population mean IQ score that would occur if every student took the coaching classes The classes are successful if u 100 A test is made of the hypotheses Ho 100 versus H 100 Consider three possible conclusions i The classes are successful ii The classes are not successful iii The classes might not be successful Part 1 of 2 Which of the three conclusions is best if Ho is rejected The best conclusion is i Part 1 2 Part 2 of 2 Assume that the classes are not successful Is it possible to make a Type I error Explain Choose one a type I error Choose one possible The classes are not successful when the null hypothesis is Espa 00

samples technology companies and finds that 37 of them have Twitter accounts Can she conclude that more than 75 of technology companies have Twitter accounts Use the a 0 05 level of significance with the P value method and Excel Part 1 of 5 a State the null and alternate hypotheses Ho p 0 73 H p 0 73 This hypothesis test is a right tailed Part 1 5 Part 2 of 5 test b Compute the test statistic Do not round intermediate steps Round the answer to two decimal places Espa ol E 40 da

How many computers In a simple random sample of 195 households the sample mean number of personal computers was 2 82 Assume the population standard deviation is a 0 53 Part 1 of 4 a Construct a 99 8 confidence interval for the mean number of personal computers Round the answer to at least two decimal places A 99 8 confidence interval for the mean number of personal computers is 2 703 2 937 Part 1 4 Part 2 of 4 b If the sample size were 165 rather than 195 would the margin of error be larger or smaller than the result in part a Explain The margin of error would be Choose one since Choose one in the sample size will Choose one the standard error Espa ol

b A new sample of 83 adults is drawn Find the probability that more than 41 of the people in this sample have high blood pressure Round the answer to at least four decimal places The probability that more than 41 of the people in this sample have high blood pressure is 0 0144 Part 2 5 Part 3 of 5 c Find the probability that the proportion of individuals the sample of 83 who have high blood pressure is between 0 20 and 0 32 Round the answer to zt least four decimal places The probability that the proportion of individuals in the sample of 83 who have high blood pressure is between 0 20 and 0 32 is Espa ol M 0 16 00

Yes the sample size is small but we can see that the sample seems to come from a population with an approximately normal distribution Part 1 6 b Perform a hypothesis test to determine whether you can conclude that the mean score in 2019 differs from the mean score in 2018 Assume the population standard deviation is a 118 Use the a 0 10 level of significance and the P value method with the TI 84 Plus calculator State the null and alternate hypotheses Ho H This hypothesis test is a Choose one test D D CO DO X 1 H S Ella v Cla FEJ Espa ol CO

TV sets According to the Nielsen Company the mean number of TV sets in a U S household in 2013 was 2 24 Assume the standard deviation is 1 4 A sample of 90 households is drawn Part 1 of 5 Question Attemp For a What is the probability that the sample mean number of TV sets is greater than 2 Round your answer to at least four decimal places The probability that the sample mean number of TV sets is greater than 2 is 0 9481 Part 1 5 Part 2 of 55 b What is the probability that the sample mean number of TV sets is between 2 5 and 3 Round your answer to at least four decimal places The probability that the sample mean number of TV sets is between 2 5 and 3 is m

Let s go to the movies A random sample of 41 Foreign Language movies made since the year 2000 had a mean length of 112 4 minutes with a standard deviation of 13 4 minutes Part 1 of 2 a Construct a 90 confidence interval for the true mean length of all Foreign Language movies made since 2000 Round the answers to one decimal place A 90 confidence interval for the true mean length of all Foreign Language movies made since 2000 is 108 9 u 115 9 Part 1 2 Part 2 of 2 b As of November 2010 three Spider Man movies have been released and their mean length is 129 minutes Someone claims that the mean length of Spider Man movies is actually less than the mean length of all Foreign Language movies Does the confidence interval contradict this claim The confidence interval Choose one contradict this claim

1 3 4 5 6 7 8 9 10 11 There Choose one enough evidence to conclude that the mean number of days is Choose one 50 12 Business trips A sales manager believes that the mean number of days per year her company s sales representatives spend traveling is different than 50 A test is made of Ho H 50 versus H 50 The null hypothesis is rejected State an appropriate conclusion X 13 5 Espa ol 14 8E8

Part 1 of 3 a The results of a recent statewide test suggested that the proportion is 0 62 Using this estimate what sample size is needed so that the confidence interval will have a margin of error of 0 05 A sample of 743 elementary school children is needed to obtain a 99 5 confidence interval with a margin of error of 0 05 Part 1 3 Part 2 of 3 b Estimate the sample size needed if no estimate of p is available A sample of elementary school children is needed to obtain a 99 5 confidence interval with a margin of error of 0 05 80

Question 13 of 18 1 point Question Attempt 1 of 3 SAT scores The College Board reports that in 2018 the mean score on the math SAT was 527 and the population standard deviation was a 118 A random sample of 20 students who took the test in 2019 had a mean score of 550 Following is a dotplot of the 20 scores 0 Part 0 6 100 200 300 400 H a Are the assumptions for a hypothesis test satisfied 500 00000 600 00 700 No the sample size is too small and the sample does not appear to come from a population with an approximately normal distribution Yes the sample size is large enough to perform the test whether or not the population is normally distributed 800 X Ella V Espa ol 8 E dla

Part 0 4 Part 1 of 4 State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test Height and age Are older men shorter than younger men According to a national report the mean height for U S men is 69 4 inches In a sample of 119 men between the ages of 60 and 69 the mean height was x 69 3 inches Public health officials want to determine whether the mean height u for older men is less than the mean height of all adult men Assume the population standard deviation to be a 2 58 Use the a 0 05 level of significance and the P value method with the TI 84 calculator O 0 0 0 0 13 3 14 15 16 17 Espa o 18 8 Co E 9 d

Part 0 5 5 Part 1 of 5 6 7 8 9 10 11 12 TV sets According to the Nielsen Company the mean number of TV sets in a U S household in 2013 was 2 24 Assume the standard deviation is 1 4 A sample of 90 households is drawn 13 a What is the probability that the sample mean number of TV sets is greater than 2 Round your answer to at least four decimal places The probability that the sample mean number of TV sets is greater than 2 is Espa ol 14 da

5 Part 0 5 6 Part 1 of 5 7 8 9 a State the null and alternate hypotheses 10 Ho H This hypothesis test is a Choose one test 11 0 0 0 0 0 12 Tweet tweet An article reported that 73 of companies have Twitter accounts An economist thinks the percentage is higher at technology companies She samples 70 technology companies and finds that 57 of them have Twitter accounts Can she conclude that more than 73 of technology companies have Twitter accounts Use the a 0 05 level of significance with the P value method and Excel P 13 14 15 16 17 Espa ol 18 8 E 1 dla E

Part 0 2 2 Part 1 of 2 3 4 5 The best conclusion is Choose one Which of the three conclusions is best if Ho is rejected 6 X 7 8 9 IQ Scores on a certain IQ test are known to have a mean of 100 A random sample of 41 students attend a series of coaching classes before taking the test Let u be the population mean IQ score that would occur if every student took the coaching classes The classes are successful if u 100 A test is made of the hypotheses Ho 100 versus H 100 Consider three possible conclusions 1 The classes are successful II The classes are not successful iii The classes might not be successful 10 11 12 13 Espa ol 14 87

Part 0 5 Part 1 of 5 e Blood pressure High blood pressure has been identified as a risk factor for heart attacks and strokes The proportion of U S adults with high blood pressure is 0 30 A sample of 31 U S adults is chosen Use Excel as needed 12 Choose one 10 13 a Is it appropriate to use the normal approximation to find the probability that more than 47 of the people in the sample have high blood pressure If so find the probability If not explain why not It Choose one appropriate to use the normal curve since np 14 8 h 244

QUESTION 3 1 POINT Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution What is the probability that a randomly selected book has fewer than 165 pages if the mean u is 188 pages and the standard deviation o is 23 pages Use the empirical rule Enter your answer as a percent rounded to two decimal places if necessary Provide your answer below

The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg kg of mercury In Florida bass fish were collected in 51 different lakes to measure the amount of mercury in the fish from each of the 51 lakes Do the data provide enough evidence to show that the fish in all Florida lakes have a mercury level higher than the allowable amount State the random variable population parameter and hypotheses a The symbol for thiandom variable involved in this problem is The wording for the random variable in context is as follows b The symbol for the parameter involved in this problem is X The wording for the parameter in context is as follows c Fill in the correct null and alternative hypotheses Ho 1 X the mercury level in fish of a randomly selected Florida lake the mean mercury level in fish of all Florida lakes

Labor statistics indicate that 77 of all U S cashiers and servers are women A random sample of cashiers and servers in a particular metropolitan area found that 112 of 150 cashiers and 150 of 200 servers were women At the 0 05 level of significance is there sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U S population a What are the null and alternative hypotheses O Ho p 0 77 H P 0 77 Ho P 0 77 H p 0 77 Ho p 0 77 OH P 0 77 Ho p 0 77 O H p 0 77 b What is the test statistic Round to 2 decimal places c What is the p value Round to 4 decimal places d Which is the decision for the test O Fail to reject the null hypothesis O Reject the null hypothesis e What is the interpretation of the decision There IS enough evidence to REJECT the claim that a difference exists between this metropolitan area and the larger U S population There IS enough evidence to SUPPORT the claim that a difference exists between this metropolitan area and the larger U S population There IS NOT enough evidence to SUPPORT the claim that a difference exists between this metropolitan area and the larger U S population There Is NOT enough no to DEJECT