Statistics Questions

Example 2 Listed below are the number of years it took for a random sample of college students to earn bachelor s degrees Construct a 95 confidence interval estimate of the mean time required for all college students to earn bachelor s degrees Does the confidence interval contain the value of 4 years Is there anything about the data that would suggest that the confidence interval might not be a good result Assume the data is normally distributed 4 4 4 4 4 4 4 5 4 5 4 5 4 5 4 5 6 6 8 9 9 13 13 15 Use calculator or software to calculate sample mean and sample standard deviation n x S S 1a 2 n Margin of Error E 1 a 2 df Confidence interval x E

84 Consider purchasing a system of audio components con sisting of a receiver a pair of speakers and a CD player Let A be the event that the receiver functions properly throughout the warranty period A be the event that the speakers function properly throughout the warranty period and A be the event that the CD player functions properly throughout the warranty period Suppose that these events are mutually independent with P A 95 P A 98 and P A 80 a What is the probability that all three components function properly throughout the warranty period What is the probability that at least one component needs service during the warranty period b c What is the probability that all three components need service during the warranty period d What is the probability that only the receiver needs service during the warranty period e What is the probability that exactly one of the three components needs service during the warranty period f What is the probability that all three components function properly throughout the warranty period but that at least one fails within a month after the war ranty expires

5 The offices of president vice president secretary and treasurer for an environmental club will be filled from a pool of 19 candidates Eight of the candidates are members of the debate team a What is the probability that all of the offices are filled by members of the debate team b What is the probability that none of the offices are filled by members of the debate team a P all offices filled by debate team members Round to three decimal places as needed b P no offices filled by debate team members Round to three decimal places as needed 6 The pie chart to the right shows how adults rate their financial shape Suppose 18 people are chosen at random from a group of 500 What is the probability that none of the 18 people would rate their financial shape as fair Make the assumption that the 500 people are represented by the pie chart The probability that none of the 18 people would rate their financial shane as fair in M Excellent 4 Good 42 Fair 38 Poor 14 Other 2

A golf course architect has four linden trees three white birch trees and three bald cypress trees to plant in a row along a fairway In how many ways can the landscaper plant the trees in a row assuming that the trees are evenly spaced The trees can be planted in different ways

Paper size Print 2 A golf course architect has four linden trees three white birch trees and three bald cypress trees to plant in a row along a fairway In how many ways can the landscaper plant the trees in a row assuming that the trees are evenly spaced The trees can be planted in different ways There are Type a whole number 3 A class has 27 students In how many different ways can five students form a group for an activity Assume the order of the students is not important different ways that the five students can form a group for an activity eller 4 You look over the songs in a jukebox and determine that you like 16 of the 58 songs a What is the probability that you like the next four songs that are played Assume a song cannot be repeated b What is the probability that you do not like the any of the next four songs that are played Assume a song cannot be repeated a The probability that you like the next four songs that are played is Round to three decimal places as needed b The probability that you do not like any of the next four songs that are played is Round to three decimal places as needed

A DJ is preparing a playlist of 24 songs How many different ways can the DJ arrange the first six songs the playlist There are different ways that the DJ can arrange the first six songs on the playlist Type a whole number 4

Question 7 6f 15 7 Suppose X is a binomial random variable with 8 trials and success probability 0 30 Find P X 3 Round your answer to the nearest hundredths Answer Previous Answer 55

6 Using the following information answer the following Generally the population scores on an IQ test are normally distributed with a mean of 100 and a standard deviation of 15 a What is the minimum score required to be in the bottom 25 of scores I b What is the minimum score required to be in the top 20 of scores

1 Calculating Z Scores Calculate the z score for each of the following raw scores using the following information A set of data is normally distributed with a mean equal to 10 and a standard deviation equal to 3 a 2 Z score 0 0000 b 10 c 3 d 16 C I

5 Find the probability of obtaining a score at or below the following z scores a 0 08

In a large class of introductory Statistics students the professor has each person toss a coin 20 times and calculate the proportion of their tosses that were heads Complete parts a through d below The Independence Assumption The Success Failure Condition Type integers or decimals Do not round Use the graph below to describe the sampling distribution model satisfied because the sample proportions satisfied because np and nq which are both Range A Range B Range C p hat independent of each other since one sample proportion 10 Q Q C Range A which corresponds to of the proportions spans from Type integers or decimals rounded to four decimal places as needed Use ascending order d Explain how the sampling distribution model changes as the number of tosses increases of the proportions spans from and Range B which corresponds to of the proportions spans from and OA The sampling distribution model shifts to the right because the mean of the distribution will increase OB The sampling distribution model becomes narrower because the standard deviation of the distribution will decrease OC The sampling distribution model becomes wider because the standard deviation of the distribution will increase OD The sampling distribution model shifts to the left because the mean of the distribution will decrease and another sample proportion Range C which corresponds to 1 196

Hint Questions 4 and 5 You don t have to do the z score transformation since you already have a z score 4 Find the probability of obtaining a score at or above the following z scores a 1 23 b 2 50 5 Find the probability of obtaining a score at or below the following z scores

1 2 3 4 5 SUM 1 2 5 8 10 11 17 21 23 25 000000

1 2 3 4 5 SUM 3 1 2 4 5 5 23 23 22 20 12 t The correlation coefficient is round to three decimal places r Find the slope intercept and correlation coefficient and report them accurately to three decimal places The regression equation is y 2

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 Disease No Disease 56 No Exposure 24 Answer 384 Round your answer to the nearest thousandths Previous Answer 18 668

In a large class of introductory Statistics students the professor has each person toss a coin 20 times and calculate the proportion of their tosses that were heads Complete parts a through d below a Confirm that you can use a Normal model here The Independence Assumption The Success Failure Condition Type integers or decimals Do not round b Use the 68 95 99 7 Rule to describe the sampling distribution model satisfied because the sample proportions satisfied because np The Independence Assumption The Success Failure Condition Type integers or decimals Do not round Use the graph below to describe the sampling distribution model independent of each other since one sample proportion 10 and nq which are both and about 95 between and and about 99 7 between and About 68 of the students should have proportions between Type integers or decimals rounded to four decimal places as needed Use ascending order c They increase the number of tosses to 32 each Draw and label the appropriate sampling distribution model Check the appropriate conditions to justify your model Range A Range B Range C satisfied because the sample proportions satisfied because np and nq which are both p hat independent of each other since one sample proportion 10 Q qui Q another sample proportion another sample proportion

Points 0 of 1 Sa In a poll taken in December 2012 Gallup asked 1006 national adults whether they were baseball fans 47 6 said they were Almost five years earlier in February 2008 only 34 6 of a similar size sample had reported being baseball fans Complete parts a through e below a Find the margin of error for the 2012 poll if we want 90 confidence in our estimate of the percent of U S adults who are baseball fans ME Round to three decimal places as needed

For each situation described below identify the population and the sample explain what p and p represent and tell whether it is appropriate to create a one proportion z interval Complete parts a through d below What does p represent O A The proportion of institute employees whose favorite food is pizza OB The proportion of all researchers whose favorite food is pizza OC The proportion of forms returned O D The proportion of respondents whose favorite food is pizza Is it appropriate to create a one proportion z interval OA If the sample simple random sample is representative then it is appropriate to create a one proportion z interval OB It is not appropriate because there not at least 10 successes and 10 failures OC It is not appropriate because the respondents answers are independent OD It is not appropriate because this is not a simple random sample and there is a possible nonresponse bias d A college admits 1441 first year students one year and four years later 1059 of them graduate on time The college wants to estimate the percentage of all their first year student enrollees who graduate on time Identify the population Choose the correct answer below OA The 1441 students who entered that year

Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 13 days a What percentage of pregnancies should last between 271 and 282 days b At least how many days should the longest 25 of all pregnancies last c Suppose a certain obstetrician is currently providing prenatal care to 51 pregnant patients Let y represent the mean length of their pregnancies According to the Central Limit Theorem what is the distribution of this sample mean y Specify the model mean and standard deviation d What s the probability that the mean duration of these patients pregnancies will be less than 255 days a The percentage of pregnancies that should last between 271 and 282 days is Round to two decimal places as needed b The longest 25 of all pregnancies should last at least Round to one decimal place as needed c Select the correct choice below and if necessary fill in the answer box es within your choice OA A Binomial model with trials and a probability of success of days Type integers or decimals rounded to two decimal places as needed OB A Normal model with mean and standard deviation Type integers or decimals rounded to two decimal places as needed OC There is no model that fits this distribution d The probability that the mean duration of these patients pregnancies will be less than 255 days is Round to four decimal places as needed

It is assumed that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days The results shown in the accompanying analysis of pregnancies were based on this Normal model The duration may not actually follow the Normal model however Complete parts a and b below Click the icon to view the pregnancy analysis results based on the Normal model Does the result in statement i change O A No because the Normal model can still be used according to the Central Limit Theorem even if the corre O B Yes because while the Normal model can still be used the standard deviation will potentially change OC Yes because the Normal model cannot be used if the correct model is very skewed O D Yes because while the Normal model can still be used the mean will potentially change Does the result in statement ii change OA Yes because the Normal model cannot be used if the correct model is very skewed OB Yes because while the Normal model can still be used the standard deviation will potentially change Pregnancy Analysis Results i Assuming the Normal model is true 21 1 of all pregnancies last between 270 and 280 days ii Assuming the Normal model is true the longest 25 of all pregnancies will last 276 8 days or more iii Assuming the Normal model is true a sample of 60 pregnant patients will have a sampling distribution with a mean of 266 days and a standard deviation of 2 07 days OC Yes because while the Normal model can still be used the mean will potentially change OD No because the Normal model can still be used according to the Central Limit Theorem even if the correct model is very skewed Does the result in statement iii change Print Done

For each situation described below identify the population and the sample explain what p and p represent and tell whether it is appropriate to create a one proportion z interval Complete parts a through d below What does p represent OA The proportion of cars actually seen with safety problems OB The proportion of all cars with safety problems OC The standard deviation of the proportion of cars actually seen with safety problems OD The sample size What does p represent OA The sample size OB The proportion of cars actually seen with safety problems OC The proportion of all cars with safety problems O D The standard deviation of the proportion of cars actually seen with safety problems Is it appropriate to create a one proportion z interval OA It is not appropriate because the sample is a simple random sample OB It is appropriate because the sample is less than 10 of the population C It is not appropriate because the sample is less than 10 of the population

It is assumed that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days The results shown in the accompanying analysis of pregnancies were based on this Normal model The duration may not actually follow the Normal model however Complete parts a and b below Click the icon to view the pregnancy analysis results based on the Normal model OD Yes because while the Normal model can still be used the mean will potentially change Does the result in statement ii change OA Yes because the Normal model cannot be used if the correct model is very skewed OB Yes because while the Normal model can still be used the standard deviation will potentially change OC Yes because while the Normal model can still be used the mean will potentially change OD No because the Normal model can still be used according to the Central Limit Theorem even if the corre Does the result in statement iii change Pregnancy Analysis Results i Assuming the Normal model is true 21 1 of all pregnancies last between 270 and 280 days ii Assuming the Normal model is true the longest 25 of all pregnancies will last 276 8 days or more iii Assuming the Normal model is true a sample of 60 pregnant patients will have a sampling distribution with a mean of 266 days and a standard deviation of 2 07 days OA Yes because while the Normal model can still be used the mean will potentially change B No because the Normal model can still be used according to the Central Limit Theorem even if the correct model is very skewed OC Yes because while the Normal model can still be used the standard deviation will potentially change O D Yes because the Normal model cannot be used if the correct model is very skewed Print Done 1

For each situation described below identify the population and the sample explain what p and p represent and tell whether it is appropriate to create a one proportion z interval Complete parts a through d below Is it appropriate to create a one proportion z interval OA It is appropriate because the sample is less than 10 of the population OB If the sample cluster sample is representative then it is appropriate to create a one proportion z interval OC It is not appropriate because there not at least 10 successes and 10 failures OD It is not appropriate because the sample is biased and nonrandom c A research institute wants to know the eating habits of its employees to know what to serve for lunch It mails all its employees a form in which to write their favorite foods Of the 1241 forms sent out 484 are mailed back with 184 people listing pizza as their favorite food Identify the population Choose the correct answer below OA Those who mailed back the form OB The U S population OC The 1241 people who received forms O D Employees of the institute Identify the sample Choose the correct answer below 00 Those who mailed back the form

For each situation described below identify the population and the sample explain what p and p represent and tell whether it is appropriate to create a one proportion z interval Complete parts a through d below What does p represent OA The probability of a failure OB The population proportion of those who favor prayer in schools OC The proportion of people who use the internet D The proportion of those who voted in the poll who favored prayer in school What does p represent O A The proportion of those who voted in the poll who favored prayer in school OB The population proportion of those who favor prayer in schools OC The proportion of people who use the internet OD The probability of a failure Is it appropriate to create a one proportion z interval OA It is appropriate because the sample is less than 10 of the population OB If the sample cluster sample is representative then it is appropriate to create a one proportion z interval not approprinto honoure there not at least 10 successes and 10 failures

8 State the z scores that most closely approximates the following probabilities hint similar to question 7 but you have to first convert the percentage into a decimal Similar to question 7 but you do not have to solve the entire problem a A top 10 of scores b Bottom 20 of scores c Top 50 of scores 9 A physiological psychologist studied the time it took a new recreational drug to begin to influence interpersonal perception among 145 senior adults The mean time for this population was 140 seconds with a standard deviation of 25 seconds What proportion of the participants in this study took between 135 and 155 seconds before the drug started to influence their interpersonal perception 25 135 14

For each situation described below identify the population and the sample explain what p and p represent and tell whether it is appropriate to create a one proportion z interval Complete parts a through d below b A TV talk shows asks viewers to register their opinion on prayer in schools by logging on to a website Of the 598 people who voted 546 favored prayer in schools The show wants to estimate the level of support among the general public Identify the population Choose the correct answer below OA The general public OB Internet users OC Those who logged onto the website OD All U S voters Identify the sample Choose the correct answer below OA Internet users OB The general public OC All U S voters O D Those who logged onto the website What does p represent C OA The probability of a failure

Complete the statement below As the sample size increases the mean of the sampling distribution stays the same gets larger gets smaller

The owner of Cruz Wedding Photography believes that the average number of wedding bookings per year can be estimated by a triangular distribution with a minimum of 10 maximum of 22 and most likely value of 15 One of the key variables in developing his business plan is the life he can expect from a single digital single lens reflex DSLR camera before it needs to be replaced Due to heavy usage the shutter life expectancy is estimated by a normal distribution with a mean of 147 500 clicks with a standard deviation of 9 000 For each booking the average number of photographs taken is assumed to be normally distributed with a mean of 2 050 and a standard deviation of 325 Develop a simulation model using 50 trials to determine summary statistics and the distribution of the camera life in years Click the icon to view a sample of 50 simulation trial results Say the values of the shutter life in clicks the weddings per year the photos per wedding the average weddings per camera and the camera life in years are entered in cells B3 B4 B5 B6 and B8 respectively Then for the Monte Carlo simulation the shutter life is randomly generated using the Excel formula ROUND NORM INV RAND 147 500 9 000 0 and the photos per wedding is randomly generated using the Excel formula ROUND NORM INV RAND 2 050 325 0 The formula for the average weddings per camera is B3 B5 and the formula for the camera life in years is B6 B4 Type whole numbers Determine the mean standard deviation minimum and maximum of the provided sample of 50 simulation trial results The mean is Round to four decimal places as needed

For each situation described below identify the population and the sample explain what p and p represent and tell whether it is appropriate to create a one proportion z interval Complete parts a through d below a Police set up an auto checkpoint at which drivers are stopped and their cars inspected for safety problems They find that 20 of the 143 cars stopped have at least one safety violation They want to estimate the percentage of all cars that may be unsafe Identify the population Choose the correct answer below OA All car passengers OB All cars OC Those cars actually stopped at the checkpoint OD The passengers of those cars actually stopped at the checkpoint Identify the sample Choose the correct answer below OA The passengers of those cars actually stopped at the checkpoint OB Those cars actually stopped at the checkpoint OC All cars O D All car passengers What does p represent ntually seen with safety problems

The Paralyzed Veterans of America is a philanthropic organization that relies on contributions They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution To test a new campaign they recently sent letters to a random sample of 100 000 potential donors and received 4781 donations a Give a 95 confidence interval for the true proportion of those from their entire mailing list who may donate b A staff member thinks that the true rate is 4 9 Given the confidence interval you found do you find that rate plausible a What is the 95 confidence interval The 95 confidence interval is from to Round to two decimal places as needed C

U of The environmental group Oceana analyzed 1215 samples of seafood purchased across the United States and genetically compared the pieces to standard gene fragments that can identify the speci 33 1 were mislabeled a Construct a 95 confidence interval for the proportion of all seafood sold in the country that is mislabeled or misidentified b Explain what your confidence interval says about seafood sold in the country c A government spokesperson claimed that the sample size was too small relative to the billions of pieces of seafood sold each year to generalize Is this criticism valid a What is the 95 confidence interval The 95 confidence interval is from to Round to one decimal place as needed Sa

According to MarylandMatters org 77 of Marylanders are fully vaccinated for COVID 19 A college administrator in Maryland wants to test if a higher percentage of students at their institution are fully vaccinated for COVID 19 The administor randomly selects 500 students and inquires about their vaccination status 395 of the 500 surveyed indicated that they were fully vaccinated Does this provide sufficient evidence to declare that the student body has a significantly higher percentage vaccinated than the state level Ho HA A

Calculate each probability question below Each answer will require the use of the Z table provided in Canvas Be sure to show all your work for each question Also to better understand what sections are needed I suggest drawing out the normal distribution for each 3 Calculate the probability for the following raw scores when your mean is 20 and standard deviation is 5 Hint First you have to do the z score transformation a What is the probability of obtaining a score at or above a raw score of 6 b What is the probability of obtaining a score at or above a raw score of 25 Hint Questions 4 and 5 You don t have to do the z score transformation since you already have a z score 4 Find the probability of obtaining a score at or above the following z scores a 1 23

A factory is considering replacing some older machines They decided that if the proportion of defective items the machine produces is significantly more than 3 it will be replaced A sample of 500 items produced on an older machine showed that 19 of them are defective At a significance level of 10 does the factory get rid of the machine Ho HA A A z stat Round to 2 decimal places A p value Do not round A What is your decision

1 Calculating Z Scores Calculate the z score for each of the following raw scores using the following information A set of data is normally distributed with a mean equal to 10 and a standard deviation equal to 3 a 2 2 10 3 b 10 I 10 10 3 c 3 d 16

3 Assuming each outcome is equally likely in the sample space find P AUB A COB Answer Previous Answer 8

According to Maryland Matters org 77 of Marylanders are fully vaccinated for COVID 19 A college administrator in Maryland wants to test if a higher percentage of students at their institution are fully vaccinated for COVID 19 The administor randomly selects 500 students and inquires about their vaccination status 395 of the 500 surveyed indicated that they were fully vaccinated Does this provide sufficient evidence to declare that the student body has a significantly higher percentage vaccinated than the state level Ho HA 0 77 0 77

The Centers for Disease Control estimates indicate 20 percent of the U S population had a sexually transmitted infection STI on any given day in 2018 A public health researcher thinks the percent of adutls with a STI is different in their state They randomly select 850 adults and discover that 146 have a STI Is this significant evidence that the percent of adults in this state with a STI is different than 20 Let a 0 05 z stat round to 2 decimal places 2 19 p value do not round 0 0286 What is your decision Retain Ho or Reject Ho Reject Ho

You re an accounting manager A year end audit showed 7 of transactions had errors You implement new procedures Two hundred of the most recent transactions were selected and 11 had errors You want to know if the proportion of incorrect transactions decreased Which assumption or condition if any does not check out Randomization assumption Independence assumption They all check out n pz 10 and n q 10

A factory is considering replacing some older machines They decided that if the proportion of defective items the machine produces is significantly more than 3 it will be replaced A sample of 500 items produced on an older machine showed that 19 of them are defective At a significance level of 10 does the factory get rid of the machine Ho HA 0 03 0 03 z stat Round to 2 decimal places 1 0486 p value Do not round 1472 What is your decision Retain Ho or Reject Ho Reiert Ho

Question 1 of 7 1 How many outcomes are in the event B Answer B Previous Answer 04

The age when smokers first start from previous studies is normally distributed with a mean of 13 years old with a population standard deviation of 2 1 years old A survey of smokers of this generation was done to estimate if the mean age has changed The sample of 28 smokers found that their mean starting age was 14 8 years old Find the 99 confidence interval of the mean Select an answer Do not round in between steps Round answers to at least 3 decimal places

Duke s Brand Dog Treats claim to contain 186 treats in each of its jumbo packages of treats The standard deviation for the number of treats in each package is 20 you can think of this claim as representing the whole population of jumbo packages dog treats You decide to test this because you and your dog think the jumbo packages of treats contain fewer treats than the Duke brand claims You count the number of treats in a sample of 16 jumbo packages and find that their average is 82 treats per package Calculate the one sample z test to test this claim about whether your sample of dog treats reflects the population what the company claims Put your value below and round your answer to 2 decimal places

You have a distribution with the following characteristics X 127 s 29 What is the probability of finding a score in between 100 146 Write your answer below as a percentage to two decimal places do not include the symbo

You have a distribution with the following characteristics X 70 s 22 What is the z score of 84 Write your answer below to two decimal places

structions The following is the recorded arthquakes on South Carolina from August 2016 O February 2017 Use the data to find the esiduals Then draw a residual plot by hand Use he residual plot to determine if the linear model is he best regression model for this data Magnitude Depth km 1 7 1 1 1 4 0 7 0 8 1 9 1 7 1 9 1 9 2 9 0 8 1 9 3 2 4 3 4 6 3 6 9 0 9

45 How valium works Valium is a common sant and sedative A study investigated how valium works by comparing its effect on sleep in seven geneti cally modified mice and eight normal control mice There was no significant difference between the two groups The authors say that this lack of significance is related to the large inter individual variability that also reflected in the low power 20 of the test 12 a Explain exactly what power 20 against a specific alternative means b Explain in simple language why tests having low pow er often fail to give evidence against a null hypothesis even when the null hypothesis is really false c What fact about this experiment most likely ower

What is the probability of finding a score lower than a z score of 1 81 Write your answer below as a percentage to two decimal places do not include the symbol

31 Sensitive questions The 2013 Youth Risk Behavior Survey found that 349 individuals in its random sample of 1367 Ohio high school students said that they had texted or emailed while driving in the previous 30 days That s 25 5 of the sample Why is this estimate likely to be biased Do you think it is biased high or low Does the margin of error of a 95 confidence inter val for the proportion of all Ohio high school students who texted or emailed while driving in the previous 30 days allows for this bias

8 13 Number Skills of Eighth Graders Suppose that scores on the mathemat ics part of the National Assessment of Educational Progress NAEP test for eighth grade students follow a Normal distribution with standard deviation 110 You want to estimate the mean score within 10 with 90 confi dence How large an SRS of scores must you choose