Statistics Questions

A researcher studying stress is interested in the blood pressure measurements of chief executive officers CEOs of major corporations He has good reason to believe that the mean systolic blood pressure of CEOs of major corporations is more than 134 mm Hg which is the value reported in a possibly outdated journal article He plans to perform a statistical test He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 142 mm Hg and the standard deviation of the sample to be 18 mm Hg Based on this information complete the parts below a What are the null hypothesis H and the alternative hypothesis H that should be used for the test H D H 0 b Suppose that the researcher decides not to reject the null hypothesis What sort of error might he be making Choose one c Suppose the true mean systolic blood pressure of CEOs of major corporations is 146 mm Hg Fill in the blanks to describe a Type II error A Type II error would be Choose one Choose one Choose one V Choose one the hypothesis that u is when in fact is 0 0 X X OSO 9 0 020 0 0 0 S

H C d dre then simulates the scientist s sample by drawing a slip of paper from the bag noting whether it is Mutant or not then replacing the paper into the bag and drawing another paper until he has a sample of 40 He repeats this process for 50 trials and creates a dot plot showing the proportion that are Mutant from each trial Estimate values on the dot plot a range of proportions that include about 95 of the proportions from the trials 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 proportion of Mutant selected TAXI Andre then finds the mean proportion from his simulations to be 0 2195 and the standard deviation to be 0 06 How far are your values from the last question from the mean This will represent your estimated margin of error Divide the distance from the last question by the standard deviation to get the margin of error in terms of the number of standard deviations Based on Andre s simulations should the scientist feel confident that the proportion of flies is within two standard deviations of the mean for the simulations Suppose the biologist breeds 600 flies What is the minimum number of flies the biologist should expect to have the mutation based on Andre s margin of error

Product design Electricity Setup Total 20 000 50 000 520 000 Required 1 Compute a single plantwide overhead rate assuming the company allocates overhead cost based on 13 000 direct labor hours 2 Job 31 used 200 direct labor hours and Job 42 used 480 direct labor hours Allocate overhead cost to each Job using the single plantwide overhead rate from part 1 3 Compute an activity rate for each activity using activity based costing 4 Allocate overhead costs to Job 31 and Job 42 using activity based costing Activity Cost Driver Direct labor hours DLH Engineering hours EH Machine hours MH Setups Machine hours MH Setups Required 1 Required 2 Activity Assembly Product design Electricity Activity Usage Job 31 200 26 50 Complete this question by entering your answers in the tabs below Required 3 Required 4 Allocate overhead costs to Job 31 and Job 42 using activity based costing Round Activity Rate to 2 decimal places Allocate overhead to Job 31 Activity Usage Direct labor hours Job 42 480 32 60 6 30 60 2 Machine hours Answer is not complete Engineering hours S 200 00 X S Activity Rate Is 400 26 00 X 50 00 per direct labor hour per engineering hour per machine hour Allocated Cost S 6 000 1 560 100

when blindly guessing among four answers in a multiple choice test since C is more often the correct answer than either A B or D Suppose that we take a random sample of 500 correct answers from multiple choice tests for introductory college courses and obtain the information summarized by the first row of numbers in the table below These numbers are the observed frequencies for the categories A B C and D for our sample of 500 correct answers The second row of numbers contains the frequencies expected for a sample of 500 correct answers if a correct answer is equally likely to be A B C or D The bottom row of numbers contains the following value for each of the correct answer categories A B C and D So SE Observed frequency Expected frequency Expected frequency Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your fo fE responses to three or more decimal places fE Send data to Excel Observed frequency fo Expected frequency JE JE A 142 B 0 132 C 0 392 119 D 0 125 00 0 125 00 107 0 2 592 Total 500 X a Determine the type of test statistic to use 5 Part 2 Answer the following to summarize the test of the hypothesis that each of A B C and D is equally likely to be the correct answer on tests in these introductory college courses Use the 0 05 level of significance for the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the critical value Round your answer to two or more decimal places d Can we reject the hypothesis that A B C and D are equally likely to be the correct answer on tests in these introductory college courses

A biologist is breeding fruit flies to include a specific genetic mutation that will be useful in understanding memory in humans To check whether a fly has the mutation a DNA sequence is analyzed in a way that kills the fly so the biologist only wants to test a sample of the flies to estimate the proportion of flies that have the mutation The biologist selects 40 flies to sequence at random and finds that 9 of them have the genetic mutation 1 Based on this sample estimate the proportion of flies in this group that has the genetic mutation 2 The scientist is worried that only having one sample may not be reliable for estimating the proportion of flies with the mutation but does not want to sacrifice more flies to get a larger sample The proportion from the sample is a good estimate for the population proportion but it is difficult to understand the possible variability from a single value Andre has a suggestion for how to better understand the variability a Assume the sample is representative of the population of flies and create a simulation that mimics what the scientist found Andre gets 200 pieces of paper and marks 45 of them as Mutant and puts them all in a bag Since Andre decided to use 200 pieces of paper why should 45 of them be marked Mutant What are some other combinations of total number of pieces of paper and number marked Mutant that he could use

Find the mean X of the data 78 45 73 66 61 67 x Mean

I 4 Bartholomew is grocery shopping The probability that he buys chicken is 0 85 The probability that he buys beef is 0 52 The probability that he buys both is 0 42 What is the probability that he Duys chicken or beef

a Compute the z score corresponding to the individual who obtained 38 1 miles per gallon Interpret this result b Determine the quartiles c Compute and interpret the interquartile range IQR d Determine the lower and upper fences Are there any outliers Click the icon to view the data a Compute the z score corresponding to the individual who obtained 38 1 miles per gallon Interpret this result standard deviation s The z score corresponding to the individual is and indicates that the data value is Type integers or decimals rounded to two decimal places as needed MPG Data 38 5 40 1 40 6 38 1 39 3 41 5 38 0 39 1 37 3 37 5 38 2 39 6 41 6 35 9 37 7 32 3 34 3 36 2 34 4 35 3 42 1 42 6 43 7 48 8 E n W the X

thinking about marriage Over the years writers for the magazine have researched just about everything there is to research about weddings The popular conception at the magazine has been that roughly 50 of first weddings take place indoors in a church 30 take place indoors in a building other than a church and 20 take place outdoors This past week the magazine examined a random sample of 250 first weddings and found the distribution given by the first row of numbers in the table below This row contains the frequencies observed in their sample of 250 The second row of numbers gives the frequencies expected under the hypothesis that the popular conception at the magazine is correct The bottom row of numbers contains the following value for each of the wedding location categories fo fr Observed frequency Expected frequency SE Expected frequency Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your Jo FE responses to three or more decimal places JE Send data to Excel Observed frequency 10 Expected frequency JE In a church 136 0 0 Indoors but not in a church 71 75 00 0 213 Outdoors Total a Determine the type of test statistic to use 4333 0 0 250 Part 2 Answer the following to summarize the test of the hypothesis that the actual distribution of first wedding locations matches the distribution in the magazine s popular conception Use the 0 10 level of significance for the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the p value Round your answer to three or more decimal places 0 d Can we conclude that the actual distribution of location of first weddings is different from the distribution in the magazine s popular conception OYes No E

The mean finish time for a yearly amateur auto race was 186 52 minutes with a standard deviation of 0 359 minute The winning car driven by Ted finished in 185 99 minutes The previous year s race mean finishing time of 112 9 with a standard deviation of 0 137 minute The winning car that year driven by Tammy finished in 112 56 minutes Find their respective z scores Who had the more convincing victory Ted had a finish time with a z score of Tammy had a finish time with a z score of Round to two decimal places as needed

n a certain city the average 20 to 29 year old man is 72 5 inches tall with a standard deviation of 3 1 inches while the average 20 to 29 year old woman is 64 1 inches tall with a standard deviation of 3 ches Who is relatively taller a 75 inch man or a 70 inch woman Find the corresponding z scores Who is relatively taller a 75 inch man or a 70 inch woman Select the correct choice below and fill in the answer boxes to complete your choice Round to two decimal places as needed is smaller than the z score for the woman OA The z score for the man OB The z score for the woman OC The Z score for the man OD The Z score for the woman is larger than the z score for the man is larger than the z score for the woman is smaller than the z score for the man so he is relatively taller so she is relatively taller so he is relatively taller so she is relatively taller

In your new role as a data analyst for a larg hospital patient outcomes at a newly built hospital Mountain View versus an existing hospital Greenside She is specifically interested in seeing whether patients who are seen for heart attacks are being readmitted to the hospital more often in the new facility You looked at data from a random sample of visits to the two hospitals during the last year Hospital Site Visited Was Patient Readmitted to the Hospital within 30 days following treatment for heart attack Yes No Total 7 40 O 29 63 54 00 Mountain View Greenside Total 07118 54 705 759 16 171 187 70 If you choose a person from the sample at random what is the probability that the person was readmitted to the hospital within 30 days following treatment for heart attack 876 946

Hospital administrators want to determine the average satisfaction for patients receiving care in the ER over the last month The list of all ER patients over the last month is entered into a computer program which uses an algorithm to randomly select 100 patients Surveys are then sent to those patients What type of sampling method is this O Systematic Random O Multistage cluster Simple Random

A group of 262 students was polled to determine whether they exercise regularly engaging in moderate activity for 30 60 min 3 or more times per week Exercises Regularly No Yes Total 50 38 49 62 Female O 54 31 O 61 70 72 58 130 Gender Male 96 36 132 Total 168 If you choose a person from the survey at random what is the probability that the person is male 94 262

Which of the following is concerned with monitoring estimates of present performance and predictions of future performance O Construct validity Criterion validity O Content validity O Internal validity

Researchers want to determine the percentage of students who own iPhones and Android cell phones They go to a popular spot on campus and ask first 100 students who pass what type of cell phone they own What type of sampling method is this Convenience O Stratified O Random O Cluster

In a box there are 8 red 7 blue and 6 green balls One ball is picked up randomly What is the probability that it is neither red nor green O 14 21 O 3 4 O 1 3 O 7 19

True or False reliability refers to whether we are truly measuring what we are trying to measu True False

educational backgrounds of the channel s viewers are different from the educational backgrounds of American adults ages 25 and over as a whole The executives have the following information on the American adult population as a whole obtained from a recent U S Current Population Survey Highest degree earned Less than high school High school College Higher than college Percent of population 8 The executives also obtained data from telephone surveys on highest degrees earned for a random sample of 150 American adults who are Thinking Channel viewers These data are summarized by the first row of numbers in the table below These numbers are the frequencies for the degree categories that were observed in the sample of 150 The second row of numbers gives the expected frequencies under the assumption that the distribution of highest degrees earned by Thinking Channel viewers is the same as the distribution of highest degrees earned by American adults as a whole The bottom row of numbers gives the following value for each of the degree categories fo SE Observed frequency Expected frequency Expected frequency fe Send data to Excel Observed frequency fo Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your fo B responses to three or more decimal places Expected frequency JE 12 fo fe JE Less than high school 13 0 High school 25 27 0 10 College 101 82 50 55 4 148 a Determine the type of test statistic to use Higher than college 9 12 00 0 750 Total 150 Part 2 Answer the following to summarize the test of the hypothesis that the distribution of highest degrees earned by Thinking Channel viewers is the same as the distribution of highest degrees earned by American adults as a whole Use the 0 10 level of significance for the test X Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the critical value Round your answer to two or more decimal places 0 d Can we conclude that the distribution of highest degrees earned by Thinking Channel viewers is different from the distribution of highest degrees earned by American adults as a whole As

Which of the following are TRUE about the sampling frame choose one or more Osampling frame enumerated list of population It is the group from which the sample is drawn sampling frame a summary of the sample that is drawn from the population The registrar at ASU could provide a sampling frame of the population of current ASU students

True or False the probability of an outcome can be a negative number O True False

common during some parts of the year than others Owners of a children s toy store chain asked this question Some data collected by the chain are summarized in the table below The data were obtained from a random sample of 190 people The birthdate of each person was recorded and each of these dates was placed into one of four categories winter December 21 March 20 spring March 21 June 20 summer June 21 September 20 and fall September 21 December 20 The numbers in the first row of the table are the frequencies observed in the sample for these season categories The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year The bottom row of numbers gives the following value for each of the season categories So Se JE Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your Jo JE responses to three or more decimal places fe Send data to Excel Observed frequency lo Expected frequency JE Observed frequency Expected frequency Expected frequency So Se fe Winter Spring Summer 35 0 0 45 0 0 44 47 50 0 258 Fall Total 66 47 50 7 205 a Determine the type of test statistic to use 190 X Part 2 Answer the following to summarize the test of the hypothesis that birthdays are equally likely during each season of the year Use the 0 05 level of significance the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the p value Round your answer to three or more decimal places 0 d Can we reject the hypothesis that birthdays are equally likely during each season of the year 6 E

The Ellington Dukes team AS WIL other minor league teams the Dukes rely heavily on promotions to bring fans to the ballpark These promotions are typically aimed at fans of specific ages The management for the Dukes has planned its current promotional schedule according to the following estimates 15 of fans attending Dukes games are ages o to 12 10 are ages 13 to 18 30 are ages 19 to 35 25 are ages 36 to 5s and 20 are over 55 A statistical consulting firm for the Dukes surveyed a random sample of 200 fans attending Dukes games in order to see if these estimates are accurate For the sample of 200 the observed frequency of each age category is given in the top row of numbers in the table below The second row of numbers contains the frequencies expected for a random sample of 200 fans if the Dukes management s estimates are accurate The bottom row of numbers contains the following value for each of the age categories fo E Observed frequency Expected frequency Expected frequency Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your Jo 18 2 responses to three or more decimal places Send data to Excel Observed frequency fo Expected frequency JE SE o to 12 34 13 to 18 28 0 19 to 35 61 60 00 0 017 36 to 55 30 50 00 8 000 Over 55 a Determine the type of test statistic to use 47 40 00 1 225 Total 200 X Part 2 Answer the following to summarize the test of the hypothesis that the management s estimates are accurate Use the 0 10 level of significance for the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the critical value Round your answer to two or more decimal places 0 S d Can we conclude that the management s original estimates for the age distribution of fans attending Dukes games are inaccurate OYes No X

The weight of an organ in adult males has a bell shaped distribution with a mean of 310 grams and a standard deviation of 45 grams Use the empirical rule to determine the following a About 95 of organs will be between what weights b What percentage of organs weighs between 175 grams and 445 grams c What percentage of organs weighs less than 175 grams or more than 445 grams d What percentage of organs weighs between 175 grams and 400 grams

mean hourly wage of foodservice workers in the U S this year The mean hourly wage last year was 8 25 and there is good reason to believe that this year s value is different from last year s The union decides to do a statistical test to see if the value has indeed changed The union chooses a random sample of this year s wages computes the mean of the sample to be 7 85 and computes the standard deviation of the sample to be 1 25 Based on this information complete the parts below a What are the null hypothesis H and the alternative hypothesis H that should be used for the test Ho D H 0 b Suppose that the union decides not to reject the null hypothesis What sort of error might it be making Choose one c Suppose the true mean hourly wage for foodservice workers in the U S this year is 8 25 Fill in the blanks to describe a Type I error A Type I error would be Choose one Choose one Choose one equal to 1 25 equal to 7 85 equal to 8 25 not equal to 8 25 less than 1 25 the hypothesis that u is Choose one when in fact is H 0 0 ORO X X OSO 0 0 O 0

Does it seem to you that people tend to be absent more on some days of the week than on others Recently a major biotechnology firm collected data with the hope of determining whether or not its employees were more likely to be absent on some weekdays than on others The firm examined a random sample of 100 employee absences The distribution of these 100 absences is shown in the table below The observed frequency for each category each weekday is shown in the first row of numbers The second row of numbers contains the frequencies expected for a sample of 100 employees if employee absences at the firm are equally likely on each of the five weekdays The bottom row of numbers contains the following value for each of the categories fo fe fe Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your fo fe responses to three or more decimal places JE Send data to Excel Observed frequency fo Observed frequency Expected frequency Expected frequency fo 12 SE Monday Tuesday Wednesday Thursday Friday 26 Expected frequency 0 SE 0 14 20 00 1 800 16 20 00 0 800 20 a Determine the type of test statistic to use 24 0 20 00 0 800 Total 100 X Part 2 Answer the following to summarize the test of the hypothesis that employee absences at this firm are equally likely on each of the five weekdays Use the 0 10 level of significance for the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the p value Round your answer to three or more decimal places 0 5 d Can we conclude that absences by the firm s employees are more likely on some day s of the week than on others OYes No X G A M

Macy is studying graphs of functions y fx Each set in the table contair some points on a particular graph Decide whether each set of points MIGHT BE on the graph of a function o CANNOT BE on the graph of a function 3 3 0 0 3 3 6 6 9 9 3 0 0 0 3 0 0 6 9 0 0 3 0 0 0 3 0 6 0 9 Yes O O No O

who support stricter gun control laws has been 52 A recent Gallup Poll of 1011 people showed 495 in favor of stricter gun control laws Assume the poll was given to a random sample of people Test the claim that the proportion of those favoring stricter gun control has changed Perform a hypothesis test using a significance level of 0 05 See page 405 for guidance Choose one of the following conclusions i The percentage is not significantly different from 52 A significant difference is one for which the p value is less than or equal to 0 050 The percentage is significantly different from 52

7 3 x vs Two symbols are used for the mean and x a Which represents a parameter and which a statistic b In determining the mean age of all students at your school you survey 30 students and find the mean of their ages Is this mean x or

bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 0000 T T 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 A resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math class In the class are three juniors and two seniors Using numbers 1 2 and 3 to represent juniors and 4 and 5 to represent seniors sample with out replacement Draw a sample of two people four times once in each of parts a b c and d and then fill in the following table 7 28 ESP Again In the graph for Exercise 7 27 explain how you can tell from the shape of the graphs which has the largest sample size and which has the smallest sample size 7 29 Standard Error Which of the dotplots given in Exercise 7 27 has the largest standard error and which has the smallest stan dard error 7 30 Bias Assuming that the true proportion of success for the trials shown in the graph for Exercise 7 27 is 0 2 explain whether any of the graphs shows bias a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his or her proportion of successes should be about 0 20 give or take some 7 31 Fair Coin One of the graphs shows the proportion of heads from flipping a fair coin 10 times repeatedly The others do not Which graph represents the coin flips Explain how you know SECTION EXERCISES CHAPTER7 7 32 Far from Fair Which of the graphs in Exercise 7 31 is centered farthest from 0 50 Repetition 1 from part a 2 from part b 3 4 a Use the first line reprinted here from the random number table to select your sample of two The selections are underlined 02779 72645 32699 86009 Report the percentage of seniors in the sample Count the number of 4 s and 5 s and divide by the sample size 2 b Use the next line to select your sample of two 31867 85872 91430 45554 Report the percentage of seniors in the sample c Use the next line to select your sample of two 07033 75250 34546 75298 Report the percentage of seniors in the sample d Use the last line to select your sample of two 09541 09084 98948 Report the percentage of seniors in the sample e Fill in the rest of the table below showing the results of the four samples p Population Proportion of Seniors 2 5 0 4 347 80623 p Sample Proportion of Seniors 1 2 0 5 Error p p 0 5 0 4 0 1 7 34 Simulation From a very large essentially infinite population of which half are men and half are women you take a random sample with replacement Use the following random number table and assume each single digit represents selection of one person the odd numbers represent women and the even numbers 0 2 4 6 8 men a Start on the left side of the top line with 118 and count 10 people What percentage of the sample will be men

8 2 Choose one of the answers in each case In statistical infer ence measurements are made on a sample or population and generalizations are made to a sample or population

on your jury CTION 7 2 Targets Bias or Lack of Precision If a rifleman s gunsight is adjusted incorrectly he might shoot bullets consistently close to 2 feet left of the bull s eye target Draw a sketch of the target with the bullet holes Does this show lack of precision or bias Draw a second sketch of the target if the shots are both unbiased and precise have little variation The rifleman s aim is not perfect so your sketches should show more than one bullet hole Targets Bias or Lack of Precision Again If a rifleman s gunsight is adjusted correctly but he has shaky arms the bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 HL 0000000 oooo amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math cla the class are three juniors and two seniors Using numbers 1 3 to represent juniors and 4 and 5 to represent seniors sampl out replacement Draw a sample of two people four times or each of parts a b c and d and then fill in the following tab a Use the first line reprinted here from the random number tabl select your sample of two The selections are underlined 02779 72645 32699 86009 Report the percentage of seniors in the sample Count the num 4 s and 5 s and divide by the sample size 2 7 26 Random Letters Samuel Morse suggested in the nineteent century that the letter t made up 9 of the English language Assume this is still correct A random sample of 1000 letters is take from a randomly selected large book and the t s are counted a What value should we expect for our sample percentage of t s b Calculate the standard error c Use your answers to fill in the blanks We expect t s give or take 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion 7 27 ESP A Zener deck of cards has cards that show one of five different shapes with equal representation so that the probability c selecting any particular shape is 0 20 A card is selected randomly and a person is asked to guess which card has been chosen The graph below shows a computer simulation of experiments in which a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his c her proportion of successes should be about 0 20 give or take som SECTION EXERCISES CHAPTER 7 7 32 Far from Fair Which of the graphs in Exercise 7 31 centered farthest from 0 50 b Use the next line to select your sample of two 31867 91430 45554 85872 Report the percentage of seniors in the sample c Use the next line to select your sample of two 07033 75298 75250 34546 Report the percentage of seniors in the sample d Use the last line to select your sample of two 09084 80623 98948 09541 Report the percentage of seniors in the sample e Fill in the rest of the table below showing the results of the four samples p Population p Sample

8 1 Choose one of the answers given The null hypothesis is sample statistic or always a statement about a population parameter

7 60 Human Cloning In a Gallup Poll 441 of 507 adults said it was morally wrong to clone humans a What proportion of the respondents believed it morally wrong to clone humans b Find a 95 confidence interval for the population proportion who believed it is morally wrong to clone humans Assume that Gallup used a simple random sample c Find an 80 confidence interval using a z of 1 28 if you are calculat ing by hand d Which interval is wider and why

8 7 Heart Attack Prevention A new drug is being tested to see whether it can reduce the chance of heart attack in people who have previously had a heart attack The rate of heart attack in the popula tion of concern is 0 20 The null hypothesis is that p the population proportion using the new drug that have a heart attack is 0 2 Pick the correct alternative hypothesis i p 0 2 ii p 0 2 iii p 0 2

7 2 Sample vs Census Explain the difference between a sample and a census Every 10 years the U S Census Bureau takes a census What does that mean

7 5 Ages of Presidents Suppose you knew the age at inaugu ration of all the past U S presidents Could you use those data to make inferences about ages of past presidents Why or why not

8 8 Stroke Survival Rate The proportion of people who live after suffering a stroke is 0 85 Suppose there is a new treatment that is used to increase the survival rate Use the parameter p to represent the population proportion of people who survive after a stroke For a hypothesis test of the treatment s effectiveness researchers use a null hypothesis of p 0 85 Pick the correct alternative hypothesis i p 0 85 ii p 0 85 iii p 0 85

8 6 Water A friend is tested to see whether he can tell bottled water from tap water There are 30 trials half with bottled water and half with tap water and he gets 18 right a Pick the correct null hypothesis 0 50 ii p 0 60 i p iii p 0 50 b Pick the correct alternative hypothesis i p 0 50 ii p 0 875 iii p 0 50 iv p 0 60 iv p 0 875

a If a rifleman s gunsight is adjusted correctly but he has shaky arms the bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 1 amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 A resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math class In the class are three juniors and two seniors Using numbers 1 2 and 3 to represent juniors and 4 and 5 to represent seniors sample with out replacement Draw a sample of two people four times once in each of parts a b c and d and then fill in the following table reprinted here from the random number table to select your sample of two The selections are underlined Use the 02779 72645 32699 86009 Report the percentage of seniors in the sample Count the number of 4 s and 5 s and divide by the sample size 2 C T 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion 7 28 ESP Again In the graph for Exercise 7 27 explain how you can tell from the shape of the graphs which has the largest sample size and which has the smallest sample size 7 29 Standard Error Which of the dotplots given in Exercise 7 27 has the largest standard error and which has the smallest stan dard error 7 30 Bias Assuming that the true proportion of success for the trials shown in the graph for Exercise 7 27 is 0 2 explain whether any of the graphs shows bias graph below shows a computer simulation of experiments in which a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his or her proportion of successes should be about 0 20 give or take some 7 31 Fair Coin One of the graphs shows the proportion of heads from flipping a fair coin 10 times repeatedly The others do not Which graph represents the coin flips Explain how you know SECTION EXERCISES 7 32 Far from Fair Which of the graphs in Exercise 7 31 is centered farthest from 0 50 CHAPTER 7 b Use the next line to select your sample of two 31867 85872 91430 45554 Report the percentage of seniors in the sample c Use the next line to select your sample of two 75250 34546 75298 Report the percentage of seniors in the sample 07033 d Use the last line to select your sample of two 98948 09541 80623 Report the percentage of seniors in the sample 09084 e Fill in the rest of the table below showing the results of the four samples Repetition 1 from part a 2 from part b 4 p Population Proportion of Seniors 2 5 0 4 347 p Sample Proportion of Seniors 1 2 0 5 Error pp 0 5 0 4 0 1 7 34 Simulation From a very large essentially infinite population of which half are men and half are women you take a random sample with replacement Use the following random number table and assume each single digit represents selection of one person the odd numbers represent women and the even numbers 0 2 4 6 8 men a Start on the left side of the top line with 118 and count 10 people What percentage of the sample will be men

8 5 Magic A magician claims he can cause a coin to come up heads more than 50 of the time A coin is flipped 40 times and 35 heads come up a Pick the correct null hypothesis i P 0 50 ii p 0 875 b Pick the correct alternative hypothesis i p 0 50 iii p 0 50 ii p 0 875 iii p 0 50 iv p 0 875 iv p 0 875

7 6 Heights of Basketball Team Suppose you find all the heights of the members of the men s basketball team at your school Could you use those data to make inferences about heights of all men at your school Why or why not

TRY 7 1 Parameter vs Statistic Example 1 Explain the differ ence between a parameter and a statistic

7 4 x vs The mean GPA of all 5000 students at Uneeda College is 2 78 A sample of 50 GPAs from this school has a mean of 2 93 Which number is and which is x

during the fall and Spring semesters If there are 197 full time teaching positions available for apportionment among the three departments based on course enrollment answer each of the following questions a Subject History Liberal Arts Math English Subject History Liberal Arts Math English Subject Find the number of teaching positions that should be apportioned to each department in the fall using Jefferson s Method History Liberal Arts Math English C Standard Quota Lower Quota Standard Quota Fall 1902 6 14200 3898 Modified Quota if needed New Lower Quota b Find the number of teaching positions that should be apportioned to each department in the fall using Hamilton s Method Lower Quota Additional based on decimals Spring 1922 118 14200 3938 New Doundod Modified Quota if needed Find the number of teaching positions that should be apportioned to each department in the fall using Webster s Method Subject Standard Rounded Modified New Lower Quota Final allocation Modified Quota lif New Rounded

Toll Payment Method E Z Pass Cash Total Cars 527 935 1462 Trucks 316 683 999 Total 843 1618 2461 EZPass AND TICKETS 3 00 EZPass AND TICKETS 2 EZPass ONLY 11 EZPass AND TICKETS Based on the this data what is the probability that the first THREE vehicles passing through this toll station

C Use comparative or superlative form of the adjectives A a daki c mleleri s fatlar n st nl k veya en st nl k halleriyle tamamlay n z 25P 1 Mount Everest is 2 My brother is the 3 Your father isn t 4 Her English is 5 August is the than Mount A ri high student in the class handsome than my father rich than her brother s good month of the year hot

its customers driving records updating its rates according to the trends indicated by these records AutoWrecks records indicate that in a typical year roughly 70 of the company s customers do not commit a moving violation 10 commit exactly one moving violation 15 commit exactly two moving violations and 5 commit three or more moving violations This past year s driving records for a random sample of 100 AutoWrecks customers are summarized by the first row of numbers in the table below That row gives this year s observed frequency for each moving violation category for the sample of 100 AutoWrecks customers The second row of numbers gives the frequencies expected for a sample of 100 AutoWrecks customers if the moving violations distribution for this year is the same as the distribution for a typical year The bottom row of numbers contains the following value for each of the moving violation categories fo fe Observed frequency Expected frequency Expected frequency Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your SO SE responses to three or more decimal places SE Send data to Excel Observed frequency So Expected frequency JE Jo JE JE No violations 62 0 0 Exactly one violation 10 10 00 0 000 Exactly two violations 21 0 Three or more violations a Determine the type of test statistic to use 7 5 00 0 800 Total 100 Part 2 Answer the following to summarize the test of the hypothesis that there is no difference between this year s moving violation distribution and the distribution in a typical year Use the 0 10 level of significance for the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the p value Round your answer to three or more decimal places 0 d Can we reject the hypothesis that there is no difference between this year s moving violation distribution and the distribution in a X

The following contingency table gives a summary of the data from 2000 trials of a visual experiment Each of the trials was classified according to two variables color vision of the participant Colorblind or Not colorblind and trial outcome Hit Miss False alarm or Correct rejection In the cells of the table are the respective observed frequencies and three of the cells also have blanks Fill in these blanks with the frequencies expected if the two variables color vision of participant and trial outcome are independent Round your answers to two or more decimal places Send data to Excel Colorblind Color vision of Not participant colorblind Total Hit 58 628 686 Miss 38 268 306 Trial outcome False Correct alarm rejection 23 85 283 306 617 702 Total 204 1796 2000 X

A consumer response team hears directly from consumers about the challenges they face in the marketplace brings their concerns to the attention of financial institutions and assists in addressing their complaints The consumer response team accepts complaints related to mortgages bank accounts and services private student loans other consumer loans and credit reporting An analysis of complaints over time indicates that the mean number of credit reporting complaints registered by consumers is 3 35 per day Assume that the number of credit reporting complaints registered by consumers is distributed as a Poisson random variable Complete parts a through d below a What is the probability that on a given day no credit reporting complaints will be registered by consumers The probability that no complaints will be registered is Round to four decimal places as needed b What is the probability that on a given day exactly one credit reporting complaint will be registered by consumers The probability that exactly one complaint will be registered is Round to four decimal places as needed c What is the probability that on a given day more than one credit reporting complaint will be registered by consumers The probability that more than one complaint will be registered is Round to four decimal places as needed d What is the probability that on a given day fewer than two credit reporting complaints will be registered by consumers The probability that fewer than two complaints will be registered is Round to four decimal places as needed