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Elementary Statistics 12th Edition Mario F. Triola - Solutions

Repeat Exercise 5 using the volumes (oz) of cans of diet Coke. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim.
Data Set 21 in Appendix B includes a simple random sample of “wheat” pennies. U.S. Mint specifications now use a standard deviation of 0.0230 g for weights of pennies. Use a 0.01 significance level to test the claim that wheat pennies were manufactured so that their weights have a standard
For large numbers of degrees of freedom, we can approximate critical values of x2 as follows:Here k is the number of degrees of freedom and z is the critical value(s) found from technology or table A-2. In Exercise 5 we have df = 35, so table A-4 does not list an exact critical value. If we want to
Repeat Exercise 19 using this approximation (with k and z as described in Exercise 19):
Characterize each of the following statements as being true or false. a. In a hypothesis test, a very high P-value indicates strong support of the alternative hypothesis. b. The Student t distribution can be used to test a claim about a population mean whenever the sample data are randomly selected
In a Gallulloll, 1010 adults were randomly selected and asked if they were satisfied or dissatisfied with the amount of leisure time that they had. Of this sample 657 said that they were satisfied and 353 said that they were dissatisfied. Use a 0.01 significance level to test the claim that 2/3 of
In a USA Today poll of 737 respondents, 92% said that they do not open unfamiliar e-mail and instant-message links. Use a 0.01 significance level to test the claim that more than 75% of us do not open unfamiliar e-mail and instant-message links. How is the validity of the results affected by the
A simple random sample of 1862 births of Chinese babies resulted in a mean birth weight of 3171 g and a standard deviation of 428 g (based on “Comparison of Birth Weight Distributions between Chinese and Caucasian Infants,” by Wen et al., American Journal of Epidemiology, Vol. 172, No 10). Use
A simple random sample of 81 births of Chinese babies resulted in a mean birth weight of 3245 g and a standard deviation of 466g. Test the claim that the standard deviation of birth weights of Chinese babies is equal to 567 g, which is the standard deviation of birth weights of Caucasian babies.
Listed below are measured amounts of lead (in micrograms per cubic meter, or mg/m3, in the air. The Environmental Protection Agency has established an air quality standard for lead of 1.5 mg/m3. The measurements shown below constitute a simple random sample of measurements recorded at Building 5 of
In the Pennsylvania Match 6 lottery, six numbers between 1 and 49 are randomly drawn. To simulate the number selection process, a TI-83/84 Plus calculator was used to randomly generate 100 numbers between 1 and 49 inclusive. The sample has a mean of 24.2 and a standard deviation of 14.1. Use a 0.01
a. In general, what is a type I error? In general, what is a type II error? b. For the hypothesis test in Exercise 7, write a statement that would constitute a type I error, and write another statement that would be a type II error.
Assume that we want to use the same sample data from Exercise 7 to test the claim that the standard deviation of all drawn numbers is less than 15.0. Why can’t we use a x2 test with the methods described in Section 8-4?
The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in HIC (standard head injury condition units). The safety requirement is that the HIC measurement should be less than 1000
A simple random sample of pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, is obtained. Listed below are the numbers of words defined on those pages. Find the values of the indicated statistics. 51 63 36 43 34 62 73 39 53 79 a. Mean b. Median c. Standard deviation d. Variance
Refer to the sample data in Exercise 1. a. What is the level of measurement of the data (nominal, ordinal, interval, ratio)? b. Are the values discrete or continuous? c. What does it mean to state that the sample is a simple random sample?
Use the sample values given in Exercise 1 to construct a 95% confidence interval estimate of the population mean. Assume that the population has a normal distribution.
Refer to the sample data given in Exercise 1. Given that the dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is the same as the claim that the mean number of defined words on a page is greater than 48.0. Use a 0.05 significance level to test the
The sitting height (from seat to top of head) of drivers must be considered in the design of a new car model. Men have sitting heights that are normally distributed with a mean of 36.0 in. and a standard deviation of 1.4 in. (based on anthropometric survey data from Gordon, Churchill, et al.). a.
Among Americans, 9.7% of males are left-handed and 12.5% of females are left-handed. a. If three females are randomly selected, find the probability that they are all left-handed. When randomly selecting three females, is it unlikely that all of them are left-handed? Why or why not? b. If one male
The accompanying graph depicts results from a recent year in which there were 8878 male graduates and 8203 female graduates from medical schools in the United States. Does the graph depict the data in a way that is fair and objective, or is it somehow deceptive? Explain.
In a recent Galluppoll, 1003 randomly selected adults in the United States were asked if they have a gun in their home, and 37.2% of them answered “yes.” a. What is the number of respondents who answered “yes”? b. Construct a 95% confidence interval estimate of the percentage of all adults
Refer to the survey results from Exercise 9 and use a 0.01 significance level to test the claim that fewer than 50% of Americans say that they have a gun in their home.
In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and
For the sample data given in Exercise 1, consider the Salk vaccine treatment group to be the first sample. Identify the values of n1, p̂1, Q` n1, n2, p̂2, Q` n2, p, and q. Round all values so that they have six significant digits.
Refer to the hypothesis test described in Exercise 1. a. Identify the null hypothesis and the alternative hypothesis. b. If the P-value for the test is reported as “less than 0.001,” what should we conclude about the original claim?
a. Assume that we want to use a 0.05 significance level to test the claim that p1 < p2. If we want to test that claim by using a confidence interval, what confidence level should we use? b. If we test the claim in part (a) using the sample data in Exercise 1, we get this confidence interval:
A USA Today article about an experimental nasal spray vaccine for children stated, “In a trial involving 1602 children only 14 (1%) of the 1070 who received the vaccine developed the flu, compared with 95 (18%) of the 532 who got a placebo.” The accompanying TI-83/84 Plus calculator display
Among 436 workers surveyed in a Gallup poll, 192 said that it was seriously unethical to monitor employee e-mail. Among 121 senior-level managers, 40 said that it was seriously unethical to monitor employee e-mail. Consider the claim that for those saying that monitoring e-mail is seriously
A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white. We want to use a 0.01 significance level to test the
The herb ginkgo Biloba is commonly used as a treatment to prevent dementia. In a study of the effectiveness of this treatment, 1545 elderly subjects were given ginkgo and 1524 elderly subjects were given a placebo. Among those in the ginkgo treatment group, 246 later developed dementia, and among
A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. We want to use a 0.05 significance level to test the claim that seat belts are effective in
A study investigated survival rates for in-hospital patients who suffered cardiac arrest. Among 58,593 patients who had cardiac arrest during the day, 11,604 survived and were discharged. Among 28,155 patients who suffered cardiac arrest at night, 4139 survived and were discharged. We want to use a
Rhino viruses typically cause common colds. In a test of the effectiveness of Echinacea, 40 of the 45 subjects treated with Echinacea developed rhinovirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections. We want to use a 0.05 significance level to test the
In a randomized controlled trial in Kenya, insecticide treated bednets were tested as a way to reduce malaria. Among 343 infants using bednets, 15 developed malaria. Among 294 infants not using bednets, 27 developed malaria. We want to use a 0.01 significance level to test the claim that the
Since the Hawk-Eye instant replay system for tennis was introduced at the U.S. Open in 2006, men challenged 1412 referee calls, with the result that 421 of the calls were overturned. Women challenged 759 referee calls, and 220 of the calls were overturned. We want to use a 0.05 significance level
In a study of police gunfire reports during a recent year, it was found that among 540 shots fired by New York City police, 182 hit their targets; and among 283 shots fired by Los Angeles police, 77 hit their targets. We want to use a 0.05 significance level to test the claim that New York City
In a study of treatments for very painful “cluster” headaches, 150 patients were treated with oxygen and 148 other patients were given a placebo consisting of ordinary air. Among the 150 patients in the oxygen treatment group, 116 were free from headaches 15 minutes after treatment. Among the
In the same study cited in Example 1, another trial was conducted with 75 women in China given a 100-Yuan bill, while another 75 women in China were given 100 Yuan in the form of smaller bills (a 50-Yuan bill plus two 20-Yuan bills plus two 5-Yuan bills). Among those given the single bill, 60 spent
In a random sample of males, it was found that 23 write with their left hands and 217 do not. In a random sample of females, it was found that 65 write with their left hands and 455 do not (based on data from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education
In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also, 12,883 women finished and 163 dropped out (based on data from the New York Times). We want to use a 0.01 significance level to test the claim that the rate of those who finish is the same for men and women. a. Test
In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman, the authors consider sample data in this statement: “Independent simple random samples, each of size 200, have been drawn, and 112 people in the first
Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 2000 people with 1404 of them having the same common attribute. Compare the results from a hypothesis test of p1 = p2
Which of the following involve independent samples?a. To test the effectiveness of the Atkins diet, 36 randomly selected subjects are weighed before the diet and six months after treatment with the diet. The two samples consist of the before/after weights.b. To determine whether smoking affects
What does the confidence interval in Exercise 2 suggest about the heights of men and women?
Repeat Example 2 with these changes: Use a 0.05 significance level, and test the claim that the two samples are from populations with the same mean. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the
In the Chapter Problem, it was noted that researchers conducted a study to investigate the effects of color on cognitive tasks. Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Use a 0.05 significance
People spend around $5 million annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating Mack pain. Pain was measured using the visual analog scale, and the results given me low are among the
The accompanying table gives results from a study of the words spoken in a day by men and women, and the original data are in Data Set 17 in Appendix B. Use a 0.01 significance level to test the claim that the mean number of words spoken in a day by men is less than that for women.Assume that the
If we use the body temperatures from 8 a.m. on Day 2 as listed in Data Set 3 in Appendix B, we get the statistics given in the accompanying table. Use these data with a 0.01 significance level to test the claim that Women have a higher mean body temperature than Men.Assume that the two samples are
Consider the sample of body temperatures (°F) listed in the last column of Data Set 3 in Appendix B. The summary statistics are given in the accompanying table. Use a 0.01 significance level to test the claim that men and women have different mean body temperatures.Assume that the two samples
Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below (based on data from Ancient Races of the Thebaid, by Thomson and Randall-Maciver, Oxford University Press). Use a 0.01 significance level to test
Data Set 15 in Appendix B lists arrival delay times (min) for randomly selected flights from New York (JFK) to Los Angeles (LAX). Statistics for times are given below. Use a 0.05 significance level to test the claim that Flight 1 and Flight 3 have the same mean arrival delay time.Assume that the
Tests In a study of proctored and nonproctored tests in an online Intermediate Algebra course a, researchers obtained the data for test results given below Use a 0.01 significance level to test the claim that students taking nonproctored tests get a higher mean than those taking proctored
Tests In the same study described in the preceding exercise, the same groups of students took a nonproctored test; the results are given below. Use a 0.01 significance level to test the claim that the samples are from populations with the same mean.Assume that the two samples are independent simple
We know that the mean weight of men is greater than the mean weight of women, and the mean height of men is greater than the mean height of women. A person€™s body mass index (BMI) is computed by dividing weight (kg) by the square of height (m). Given below are the BMI statistics for random
Data Set 5 in Appendix B lists full IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The statistics are summarized below. Use a 0.05 significance level to test the claim that the mean IQ score
Repeat Exercise 16 after replacing the low lead level group with the following full IQ scores from the medium lead level group.Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations
Listed below are the heights (inches) for the simple random sample of supermodels Lima, Bundchen, Ambrosio, Ebanks, Iman, Rubik, Kurkova, Kerr, Kroes, and Swanepoel. Data Set 1 in Appendix B includes the heights of a simple random sample of 40 women from the general population, and here are the
Listed below are the numbers of years that popes and British monarchs (since 1690) lived after their election or coronation. Treat the values as simple random samples from a larger population. Use a 0.01 significance level to test the claim that the mean longevity for popes is less than the mean
Listed below are amounts of strontium-90 in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born after 1979. Use a 0.05 significance level to test the claim that the mean amount of strontium-90 from Pennsylvania residents is greater than the mean
Vending machines reject coins based on weight. Refer to Data Set 21 in Appendix B and use a 0.05 significance level to test the claim that the mean weight of pre-1964 quarters is equal to the mean weight of post-1964 quarters. Given the relatively small sample sizes from the large populations of
Reports of results from clinical trials often include statistics about “baseline characteristics,” so we can see that different groups have the same basic characteristics. Refer to Data Set 1 in Appendix B and construct a 95% confidence interval estimate of the difference between the mean age
Refer to Data Set 19 in Appendix B and construct a 95% confidence interval estimate of the difference between the mean weight of the cola in cans of regular Pepsi and the mean weight of cola in cans of Diet Pepsi. Does there appear to be a difference between those two means? If there is a
Refer to Data Set 19 in Appendix B and use a 0.05 significance level to test the claim that because they contain the same amount of cola, the mean weight of cola in cans of regular Coke is the same as the mean weight of cola in cans of Diet Coke. If there is a difference in the mean weights,
Do Men Have a Higher Mean Body Temperature? Repeat Exercise 9 with the additional assumption that σ1 = σ2. How are the results affected by this additional assumption? Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that
Repeat Exercise 8 with the additional assumption that σ1 = σ2. How are the results affected by this additional assumption? Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are
An experiment was conducted to test the effects of alcohol. Researchers measured the breath alcohol levels for a treatment group of people who drank ethanol and another group given a placebo. The results are given below. Use a 0.05 significance level to test the claim that the two sample groups
The confidence interval given in Exercise 2 is based on df = 39, which is the “smaller of n1 — 1 and n2 — 1.” Use Formula 9-1 to find the number of degrees of freedom. Using the number of degrees of freedom from Formula 9-1 results in this confidence interval: 11.65 cm < µ1< µ2< 17.28 cm.
We sometimes know the value of one population standard deviation from an extensive history of data, but a new procedure or treatment results in sample values with an unknown standard deviation. If Ïƒ1 is known but Ïƒ2 is unknown, use the procedures in Part 1 of this section with these changes:
If we use the sample data in Exercise 2, we get this 95% confidence interval estimate: 1.0 mi/gal < µd< 3.8 mi/gal. Treating the same data as independent samples yields —7.8 mi/gal < µ1 - µ2< 12.6 mi/gal for a 95% confidence level. What is the difference between interpretations of these two
Test Example 1 in this section used only five pairs of data from Data Set 12 in Appendix B for a 95% confidence level. Repeat Example 1 using all of the cases with heights for both the president and the main opponent. Results are shown in the accompanying TI-83/84 Plus calculator display.
Confidence Interval Example 2 in this section used only five pairs of data from Data Set 12 in Appendix B. Repeat Example 2 using all of the cases with heights for both the president and the main opponent. The accompanying TI-83/84 Plus calculator display shows results for a 90% confidence interval
Listed below are ages of actresses and actors at the time that they won Oscars for the categories of Best Actress and Best Actor. The data are from Data Set 11 in Appendix B.Assume that you want to use a 0.05 significance level to test the claim that paired sample data come from a population for
Listed below are body temperatures of four subjects measured at two different times in a day (from Data Set 3 in Appendix B).Assume that you want to use a 0.05 significance level to test the claim that paired sample data come from a population for which the mean difference is µd = 0. Find(a)
Oscars Use the sample data from Exercise 7 to test for a difference between the ages of actresses and actors when they win Oscars. Use a significance level of a = 0.05.Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately
Body Temperatures Use the sample data from Exercise 8 to test the claim that there is no difference between body temperatures measured at 8 A.M. and at 12 A.M. Use a 0.05 significance level.Assume that the paired sample data are simple random samples and that the differences have a distribution
Flight Operations The table below lists the times (min) required for randomly selected flights to taxi out for takeoff and the corresponding times (min) required to taxi in after landing. (See Data Set 15 in Appendix B.) All flights are Flight 1 of American Airlines from New York (JFK) to Los
Brain Volumes of Twins Listed below are brain volumes (cm3) of twins listed in Data Set 6 of Appendix B. Construct a 99% confidence interval estimate of the mean of the differences between volumes for the first-born and the second-born twins. What does the confidence interval suggest?Assume that
Speaking Couples Listed below are the numbers of words spoken in a day by each member of six different couples. The data are randomly selected from the first two columns in Data Set 17 from Appendix B. Use a 0.05 significance level to test the claim that among couples, males speak more words in a
Is Blood Pressure the Same for Both Arms? Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman (based on data from €œConsistency of Blood Pressure Differences Between the Left and Right Arms,€ by Eguchi, et al., Archives of
Is Friday the 13th Unlucky? Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month (based on data from €œIs Friday the 13th Bad for
Self-Reported and Measured Male Heights As part of the National Health and Nutrition Examination Survey, the Department of Health and Human Services obtained self-reported heights and measured heights for males aged 12€”16. All measurement are in inches. Listed below are sample results.
The Harry Potter books and movies grossed huge sums of money. The table below lists the amounts grossed (in millions of dollars) during the first few days of release of the movies Harry Potter and the Half-Blood Prince and Harry Potter and the Order of the Phoenix. Use a 0.05 significance level to
Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the accompanying table (based on data from €œEssential
A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given in the accompanying table. The values are before and after hypnosis; the measurements are in centimeters on a pain scale. Construct a 95% confidence interval for
The author recorded actual temperatures (°F) along with the temperatures (°F) that were predicted five days earlier. Results are listed below. Construct a 99% confidence interval estimate of the mean of the population of €œactual/forecast€ differences. What does the
Oscars Use the sample data from Data Set 11 in Appendix B to test for a difference between the ages of actresses and actors when they win Oscars. Use a significance level of α = 0.05. Use the indicated Data Sets from Appendix B. Assume that the paired sample data are simple random samples and the
Body Temperatures Use the sample data from 8 A.M. and 12 A.M. on Day 1 as listed in Data Set 3 in Appendix B. Test the claim that there is no difference between body temperatures measured at 8 A.M. and at 12 A.M. Use a 0.05 significance level. Use the indicated Data Sets from Appendix B. Assume
Speaking Couples Use the data in the first two columns of Data Set 17 in Appendix B. Those columns list the numbers of words spoken in a day by each member of 56 different couples. Use a 0.05 significance level. Use the indicated Data Sets from Appendix B. Assume that the paired sample data are
Refer to Data Set 8 in Appendix B and use the times (seconds) that animated Disney movies showed the use of tobacco and the times that they showed the use of alcohol. Use a 0.05 significance level to test the claim that the mean of the differences is greater than 0 sec so that more time is devoted
The “Freshman 15” refers to the urban legend that is the common belief that students gain an average of 15 lb (or 6.8 kg) during their freshman year. Refer to Data Set 4 in Appendix B and consider the sample values in this format: (April weight) — (September weight). In this format, positive
a. If s21 represents the larger of two sample variances, can the F test statistic ever be less than 1? b. Can the F test statistic ever be a negative number? c. If testing the claim that σ21 ≠ σ22 what do we know about the two samples if the test statistic is F = 1?
If using Data Set 1 in Appendix B for a test of the claim that heights of men and heights of women have different variances, we find that s = 6.60 cm for women and s = 6.02 for men.a. Find the values of s21 and s22 and express them with appropriate units of measure.b. What is the null hypothesis?c.
What does it mean when we say that the A test described in this section is not robust against departures from normality? Is the F test robust against sampling methods that do not produce simple random samples?
Students of the author randomly selected 217 student cars and recorded their ages, and they randomly selected 151 faculty cars and recorded their ages. If using the F test with these data, is it correct to reason that there is no need to check for normality because n1> 30 and n2> 30? Hypothesis
Data Set 19 in Appendix B includes the weights (in pounds) of samples of regular Coke and regular Pepsi. If we use a TI-83/84 Plus calculator to test the claim that weights of regular Coke and weights of regular Pepsi have different standard deviations, we get the results shown in the accompanying
Students of the author randomly selected 217 student cars and found that they had ages with a mean of 7.89 years and a standard deviation of 3.67 years. They also randomly selected 152 faculty cars and found that they had ages with a mean of 5.99 years and a standard deviation of 3.65 years. Using
Example 1 in this section included results from a study of the effects of color on creativity, and the results below were used to study the effects of color on cognition. Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall
The accompanying table gives results from a study of the words spoken in a day by men and women, and the original data are in Data Set 17 in Appendix B. Use a 0.05 significance level to test the claim that the numbers of words spoken in a day by men vary more than the numbers of words spoken in a

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