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elementary statistics
Questions and Answers of
Elementary Statistics
The data represent the weights (in pounds) of several professional football players. 225 250 305 285 275 265 290 310 290 250 210 225 308 325 260 165 195 245 235 298 395 255 268 190
The data represent the speeds (in miles per hour) of several vehicles. 68 88 70 72 70 69 72 62 65 70 75 52 65
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
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
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
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
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
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
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
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
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,
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
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
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
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
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,
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
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
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
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
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
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
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 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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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