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elementary statistics
Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions
75 78 80 75 62 72 74 75 80 95 76 72 In Exercises 62 and 63, use StatCrunch to (a) find the five-number summary, (b) construct a regular boxplot, and (c) construct a modified boxplot for the data.
16 9 11 12 8 10 12 13 11 10 24 9 2 15 7
Forty-three winners were older than Penelope Cruz when they won the Oscar for Best Supporting Actress. Find the percentile that corresponds to Penelope Cruz’s age.
Only three winners were younger than Heath Ledger when they won the Oscar for Best Supporting Actor. Find the percentile that corresponds to Heath Ledger’s age.
Credit Card Purchases The monthly credit card purchases (rounded to the nearest dollar) over the last two years for you and a friend are listed. You: 60 95 102 110 130 130 162 200 215 120 124 28 58 40 102 105 141 160 130 210 145 90 46 76 Friend: 100 125 132 90 85 75 140 160 180 190 160 105 145 150
Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown. (a) Describe the
21.4 20.8 19.7 15.2 31.9 18.7 15.6 16.7 19.8 13.4 22.9 28.7 19.8 17.2 30.1
12.3 9.7 8.0 15.4 16.1 11.8 12.7 13.4 12.2 8.1 7.9 10.3 11.2
23 36 47 33 34 40 39 24 32 22 38 41
5 7 1 2 3 10 8 7 5 3
Ages of Executives The ages of a sample of 100 executives are listed. 31 62 51 44 61 47 49 45 40 52 60 51 67 47 63 54 59 43 63 52 50 54 61 41 48 49 51 54 39 54 47 52 36 53 74 33 53 68 44 40 60 42 50 48 42 42 36 57 42 48 56 51 54 42 27 43 43 41 54 49 49 47 51 28 54 36 36 41 60 55 42 59 35 65 48 56
Find the z-score for a male in the 20–29 age group whose height is 66.3 inches. What percentile is this?
Find the z-score for a male in the 20–29 age group whose height is 71.1 inches. What percentile is this?
Three adult males in the 20–29 age group are randomly selected. Their heights are 70 inches, 66 inches, and 68 inches. Use z-scores to determine which heights, if any, are unusual.
Three adult males in the 20–29 age group are randomly selected. Their heights are 74 inches, 62 inches, and 80 inches. Use z-scores to determine which heights, if any, are unusual.
What percentile is a height of 77 inches? How should you interpret this?
What height represents the 60th percentile? How should you interpret this?
Life Spans of Fruit Flies The life spans of a species of fruit fly have a bellshaped distribution, with a mean of 33 days and a standard deviation of 4 days. (a) The life spans of three randomly selected fruit flies are 34 days, 30 days, and 42 days. Find the z-score that corresponds to each life
Life Spans of Tires A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. (Assume the life spans of the tires have a bell-shaped distribution.) (a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000
A student gets a 63 on the statistics test and a 23 on the biology test.
A student gets a 78 on the statistics test and a 29 on the biology test.
A student gets a 60 on the statistics test and a 22 on the biology test.
A student gets a 75 on the statistics test and a 25 on the biology test.
z=0.77 z = 1.54 z=-1.54 Biology Test Scores Number 16 14- 12 10 8- 6- 4 2 17 20 23 26 A Score (out of 30) A 29 B C
z = 0 z = 2.14 z=-1.43 Number 16 14- 12 10 8 6 Statistics Test Scores 48 53 58 63 68 73 78 + Score (out of 80) A B C
Manufacturer Earnings Refer to the data set given in Exercise 34 and the box-and-whisker plot you drew that represents the data set. (a) About 75% of the manufacturers made less than what amount per hour? (b) What percent of the manufacturers made more than $15.80 per hour? (c) If you randomly
TV Viewing Refer to the data set given in Exercise 31 and the box-andwhisker plot you drew that represents the data set. (a) About 75% of the people watched no more than how many hours of television per day? (b) What percent of the people watched more than 4 hours of television per day? (c) If
Explain how the interquartile range of a data set can be used to identify outliers.
A counselor tells a child’s parents that their child’s IQ is in the 93rd percentile for the child’s age group. What can you conclude about the child’s IQ?
A student’s score on an actuarial exam is in the 78th percentile.What can you conclude about the student’s exam score?
A salesperson at a company sold $6,903,435 of hardware equipment last year, a figure that represented the eighth decile of sales performance at the company. What can you conclude about the salesperson’s performance?
The goals scored per game by a soccer team represent the first quartile for all teams in a league. What can you conclude about the team’s goals scored per game?
Construct a population data set for which 5, and2.
Construct a sample data set for which n=7 x=9
Why is the standard deviation used more frequently than the variance? (Hint: Consider the units of the variance.)
min = 54, max = 247, 10 classes
min = 17, max = 135, 8 classes
min = 12, max = 88, 6 classes
min = 9, max = 64, 7 classes
Class boundaries are used to ensure that consecutive bars of a histogram touch. In Exercises 11–14, use the given minimum and maximum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits.
An ogive is a graph that displays relative frequencies.
The midpoint of a class is the sum of its lower and upper limits divided by two.
In a frequency distribution, the class width is the distance between the lower and upper limits of a class.
Claim: 2; a = 0.10. Sample statistics: =520, 51 2 = 500, $2 = 55, n =6.Assume variances are not equal. = 5 and =25, n = 7 and
Claim: ; a = 0.01. Sample statistics: = 61, s = 3.3, n 255, s = 1.2, n =7.Assume equal variances. == =>
Claim: = 0.01. Sample statistics: = 44.5, s = and 249.1, $25.25, n =18.Assume equal variances. == 5.85, n = 17
Claim: 2; = 0.05. Sample statistics: 183.5, s = 1.3, n = 25 and X2 = 184.7, $2 = 3.9, n225.Assume variances are not equal.
Claim: 2; a=0.10. Sample statistics: = 0.015, s = 0.011, n = 8 and 2 =0.019, s = 0.004, n =6.Assume variances are not equal.
Claim: =; = 0.05. Sample statistics: = 228, s = 27, n = 20 and 2207, $225, n =13.Assume equal variances. -
Suppose you are testing Exercise 8 at Do you still make the same decision? Explain your reasoning. =>
Suppose you are testing Exercise 7 at Do you still make the same decision? Explain your reasoning.
A government agency states that the mean annual salary of civilian federal employees is the same in California and Illinois. The mean annual salary for 180 civilian federal employees in California is $66,210 and the standard deviation is $6385.The mean annual salary for 180 civilian federal
In a fast food study, a researcher finds that the mean sodium content of 42 Wendy’s fish sandwiches is 1010 milligrams with a standard deviation of 75 milligrams. The mean sodium content of 39 Long John Silver’s fish sandwiches is 1180 milligrams with a standard deviation of 90 milligrams. At
In a fourth study conducted by the Johns Hopkins Oncology Center, the mean readability level of 137 PEMS was 11.1, with a standard deviation of 1.67. (a) Test the mean readability level of this study against the level of Study1.Use a = 0.01. (b) Test the mean readability level of this study against
Interpret the results. (See Extending Concepts in Section 8.1 Exercises.)
Construct a 95% confidence interval for M, where is the mean readability level in Study 1 and is the mean readability level in Study
Describe another way you can perform a hypothesis test for the difference between the means of two populations using large independent samples.
Explain how to perform a two-sample z-test for the difference between the means of two populations using large independent samples.
The table shows the number of larceny-thefts (per 100,000 population) and the number of motor vehicle thefts (per 100,000 population) in six randomly selected large U.S. cities. At a = 0.10, can you conclude that there is a correlation between the number of larceny-thefts and the number of motor
A meteorologist wants to determine whether days with rain occur randomly in April in his home town. To do so, the meteorologist records whether it rains for each day in April. The results are shown, where R represents a day with rain and N represents a day with no rain. At a = 0.05, can the
The table shows the sales prices for a random sample of apartment condominiums and cooperatives in four U.S. regions. At a = 0.01, can you conclude that the distributions of the sales prices in these four regions are different? (Adapted from National Association of Realtors) Region Sales Price (in
An organization claims that the median number of annual volunteer hours is 52.In a random sample of 75 people who volunteered last year, 47 volunteered for less than 52 hours, 23 volunteered for more than 52 hours, and 5 volunteered for 52 hours. At = 0.05, can you reject the organization's claim?
A labor organization claims that there is a difference in the hourly earnings of union and nonunion workers in state and local governments. A random sample of 10 union and 10 nonunion workers in state and local governments and their hourly earnings are listed in the tables. At 0.10, can you support
Describe the test statistic for the runs test when the sample sizes and are less than or equal to 20 and when either or is greater than 20
Explain, in your own words, what and represent in Example 1
What does it mean when is equal to 1? What does it mean when is equal to What does it mean when is equal to 0?
There is a difference between freshman class sizes for Massachusetts colleges and North Carolina colleges.
There is no difference between freshman class sizes for Pennsylvania colleges and California colleges.
37. The median freshman class size at a North Carolina college is different from 2400. In Exercises 6 and 7, use the Wilcoxon rank sum test to test the claim. Use a = 0.01.
36. The median freshman class size at a Pennsylvania college is 500.
35. The median freshman class size at a Massachusetts college is greater than or equal to 750.
The median freshman class size at a California college is less than or equal to 400.
Construct a side-by-side box-and-whisker plot for the four states. Do any of the median freshman class sizes appear to be the same? Do any appear to be different? In Exercises 2-5, use the sign test to test the claim. What can you conclude? Use a = 0.05.
What is the requirement for the sample size of both samples when using the Wilcoxon rank sum test?
Ages of Grooms A marriage counselor estimates that the median age of grooms at the time of their first marriage is greater than 28 years. In a random sample of 56 grooms, 33 are less than 28 years old, 23 are more than 28 years old, and none are 28 years old. At can you support the counselor’s
Ages of Brides A marriage counselor estimates that the median age of brides at the time of their first marriage is less than or equal to 26 years. In a random sample of 65 brides, 24 are less than 26 years old, 35 are more than 26 years old, and 6 are 26 years old. At can you reject the
Weekly Earnings A labor organization states that the median weekly earnings of male workers is greater than $798. To test this claim, you randomly select 70 male workers and ask each to provide his weekly earnings.The results are shown in the table.At can you support the organization’s claim?
Weekly Earnings A labor organization claims that the median weekly earnings of female workers is less than or equal to $638. To test this claim, you randomly select 50 female workers and ask each to provide her weekly earnings. The results are shown in the table. At can you reject the
Viewing Audience A television network claims that the median age of viewers for the Masters Golf Tournament is greater than 57 years. The ages of 24 randomly selected viewers are listed below. At is there enough evidence to support the network’s claim? (Adapted from ESPN) 60 85 70 59 42 21 57 25
Hourly Wages A labor organization claims that the median hourly wage of tool and die makers is $22.55. The hourly wages (in dollars) of 14 randomly selected tool and die makers are listed below. At is there enough evidence to reject the labor organization’s claim? (Adapted from U.S. Bureau of
Contacting Parents A research organization conducts a survey by randomly selecting adults and asking them how frequently they contact their parents by phone. The results are shown in the figure. (Adapted from Pew Research Center) (a) Use a sign test to test the null hypothesis that the proportion
Feeling Your Age A research organization conducts a survey by randomly selecting adults and asking them how they feel relative to their real age. The results are shown in the figure. (Adapted from Pew Research Center) (a) Use a sign test to test the null hypothesis that the proportion of adults who
SAT Scores Students at a certain school are required to take the SAT twice. The table shows both critical reading SAT scores for 12 students. At can you conclude that the students’ critical reading scores improved the second time they took the SAT?
Improving SAT Scores A tutoring agency believes that by completing a special course, students can improve their critical reading SAT scores. In part of a study, 12 students take the critical reading part of the SAT, complete the special course, then take the critical reading part of the SAT again.
Lower Back Pain The table shows the lower back pain intensity scores for 12 patients before and after taking anti-inflammatory drugs for 8 weeks.At is there enough evidence to conclude that the lower back pain intensity scores decreased after taking anti-inflammatory drugs? (Adapted from Archives
Lower Back Pain The table shows the lower back pain intensity scores for eight patients before and after receiving acupuncture for eight weeks. At is there enough evidence to conclude that the lower back pain intensity scores decreased after the acupuncture? (Adapted from Archives of Internal
Hourly Wages A labor organization estimates that the median hourly wage of podiatrists is at least $55.89. In a random sample of 23 podiatrists, 17 are paid less than $55.89 per hour, 5 are paid more than $55.89 per hour, and 1 is paid $55.89 per hour. At can you reject the labor organization’s
Hourly Wages A labor organization estimates that the median hourly wage of computer systems analysts is $37.06. In a random sample of 45 computer systems analysts, 18 are paid less than $37.06 per hour, 25 are paid more than $37.06 per hour, and 2 are paid $37.06 per hour. At can you reject the
Square Footage A renters’ organization believes that the median square footage of renter-occupied units is 1350 square feet. To test this claim, you randomly select 22 renter-occupied units and obtain the results shown above. At can you reject the organization’s claim? (Adapted from U.S. Census
Unit Size A renters’ organization claims that the median number of rooms in renter-occupied units is four. You randomly select 120 renter-occupied units and obtain the results shown below. At can you reject the organization’s claim? (Adapted from U.S. Census Bureau)
Facebook® Users A research group claims that the median age of Facebook® users is less than 32 years old. In a random sample of 20 Facebook® users, 5 are less than 32 years old, 13 are more than 32 years old, and 2 are 32 years old. At can you support the research group’s claim? (Adapted from
Twitter® Users A research group claims that the median age of Twitter® users is greater than 30 years old. In a random sample of 24 Twitter® users, 11 are less than 30 years old, 10 are more than 30 years old, and 3 are 30 years old. At can you support the research group’s claim? (Adapted from
Financial Debt A financial services accountant estimates that the median amount of financial debt for families holding such debts is less than $65,000. In a random sample of 70 families holding debts, the debts of 24 families were less than $65,000 and the debts of 46 families were greater than
Credit Card Debt A financial services institution reports that the median amount of credit card debt for families holding such debts is at least $3000. In a random sample of 104 families holding debt, the debts of 60 families were less than $3000 and the debts of 44 families were greater than
Temperature During a weather report, a meteorologist states that the median daily high temperature for the month of January in San Diego is Fahrenheit. The high temperatures (in degrees Fahrenheit) for 16 randomly selected January days in San Diego are listed below. At can you reject the
Sales Prices of Homes A real estate agent believes that the median sales price of new privately owned one-family homes sold in the past year is $198,000 or less. The sales prices (in dollars) of 10 randomly selected homes are listed below. At a = 0.05, is there enough evidence to reject the agent's
Temperature A meteorologist estimates that the median daily high temperature for the month of July in Pittsburgh is 83 Fahrenheit. The high temperatures (in degrees Fahrenheit) for 15 randomly selected July days in Pittsburgh are listed below. At a = 0.01, is there enough evidence to reject the
Credit Card Charges In order to estimate the median amount of new credit card charges for the previous month, a financial service accountant randomly selects 12 credit card accounts and records the amount of new charges for each account for the previous month. The amounts (in dollars) are listed
4. In your own words, explain why the hypothesis test discussed in this section is called the sign test.
What is a nonparametric test? How does a nonparametric test differ from a parametric test? What are the advantages and disadvantages of using a nonparametric test?
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