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Elementary Statistics 8th Edition Neil A. Weiss - Solutions

In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: “._______._______. we should be aware that, if the observed value of pˆ is closer to 0.5 than is our educated guess, the margin of
Consider a population in which the proportion of members having a specified attribute is p. Let y be the variable whose value is 1 if a member has the specified attribute and 0 if a member does not. a. If the size of the population is N, how many members of the population have the specified
x = 8, n = 40, 95% level.a. Use the one-proportion plus-four z-interval procedure, as discussed on page 449, to find the required confidence interval. b. Compare your result with the corresponding confidence interval found in Exercises 11.17–11.22, if finding such a confidence interval was
x = 10, n = 40, 90% level.a. Use the one-proportion plus-four z-interval procedure, as discussed on page 449, to find the required confidence interval. b. Compare your result with the corresponding confidence interval found in Exercises 11.17–11.22, if finding such a confidence interval was
x = 35, n = 50, 99% level.a. Use the one-proportion plus-four z-interval procedure, as discussed on page 449, to find the required confidence interval. b. Compare your result with the corresponding confidence interval found in Exercises 11.17–11.22, if finding such a confidence interval was
This exercise involves the use of an unrealistically small population to provide a concrete illustration for the exact distribution of a sample proportion. A population consists of three men and two women. The first names of the men are Jose, Pete, and Carlo; the first names of the women are Gail
x = 40, n = 50, 95% level.a. Use the one-proportion plus-four z-interval procedure, as discussed on page 449, to find the required confidence interval. b. Compare your result with the corresponding confidence interval found in Exercises 11.17–11.22, if finding such a confidence interval was
x = 16, n = 20, 90% level.a. Use the one-proportion plus-four z-interval procedure, as discussed on page 449, to find the required confidence interval. b. Compare your result with the corresponding confidence interval found in Exercises 11.17–11.22, if finding such a confidence interval was
x = 3, n = 100, 99% level.a. Use the one-proportion plus-four z-interval procedure, as discussed on page 449, to find the required confidence interval. b. Compare your result with the corresponding confidence interval found in Exercises 11.17–11.22, if finding such a confidence interval was
In the January 2009 article “Americans on Bailout: Stop Spending,” P. Steinhauser reported on a CNN/Opinion Research Corporation poll that found that, of 1245 U.S. adults sampled, 758 opposed providing more government money for the financial bailout of banks. Obtain a 95% confidence interval
A Pew Internet & American Life project examined Internet social networking by age group. According to the report, among online adults 18–24 years of age, 75% have a profile on at least one social networking site. Assuming a sample size of 328, determine a 95% confidence interval for the
In the May 2008 New York Times article “More Mothers Breast-Feed, in First Months at Least,” G. Harris reported that 77% of new mothers breast-feed their infants at least briefly, the highest rate seen in the United States in more than a decade. His report was based on data for 434 infants from
In the July 2008 article “Americans Favor Offshore Drilling,” B. Rooney reported on a CNN/Opinion Research Corporation poll that asked what Americans think about offshore drilling for oil and natural gas. Of the 500 U.S. adults surveyed, 150 said that they opposed offshore drilling. Find a 99%
Of what procedure is Procedure 11.2 a special case? Why do you think that is so?
x = 8, n = 40, H0: p = 0.3, H0: p < 0.3, α = 0.10 a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.
Repeat parts (b)-(e) of Exercise 11.5 for samples of size 1.
x = 10, n = 40, H0: p = 0.3, H0: p < 0.3, α = 0.05 a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.
x = 35, n = 50, H0: p = 0.6, H0: p > 0.6, α = 0.05 a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.
x = 40, n = 50, H0: p = 0.6, H0: p > 0.6, α = 0.01 a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.
x = 16, n = 20, H0: p = 0.7, H0: p ≠ 0.7, α = 0.05 a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.
x = 3, n = 100, H0: p = 0.04, H0: p ≠ 0.04, α = 0.10 a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.
People who were born between 1978 and 1983 are sometimes classified by demographers as belonging to Generation Y. According to a Forrester Research survey published in American Demographics (Vol. 22(1), p. 12), of 850 Generation Y Web users, 459 reported using the Internet to download music. a.
The Arizona Republic conducted a telephone poll of 758 Arizona adults who celebrate Christmas. The question asked was, “In your family, do you open presents on Christmas Eve or Christmas Day?” Of those surveyed, 394 said they wait until Christmas Daya. Determine the sample proportion. b. At the
The Substance Abuse and Mental Health Services Administration conducts surveys on drug use by type of drug and age group. Results are published in National Household Survey on Drug Abuse. According to that publication, 13.6% of 18- to 25-year-olds were current users of marijuana or hashish in 2000.
In 2006, 9.8% of all U.S. families had incomes below the poverty level, as reported by the U.S. Census Bureau in American Community Survey. During that same year, of 400 randomly selected Wyoming families, 25 had incomes below the poverty level. At the 1% significance level, do the data provide
Labor Day was created by the U.S. labor movement over 100 years ago. It was subsequently adopted by most states as an official holiday. In a Gallup Poll, 1003 randomly selected adults were asked whether they approve of labor unions; 65% said yes. a. In 1936, about 72% of Americans approved of labor
Repeat parts (b)€“(e) of Exercise 11.5 for samples of size 3. (There are 10 possible samples.)
Of the 38 numbers on an American roulette wheel, 18 are red, 18 are black, and 2 are green. If the wheel is balanced, the probability of the ball landing on red is 18/38 = 0.474. A gambler has been studying a roulette wheel. If the wheel is out of balance, he can improve his odds of winning. The
A CNN/USA TODAY/ Gallup Poll, conducted in September, 2005, had the headline “Most Americans Believe New Orleans Will Never Recover.” Of 609 adults polled by telephone, 341 said they believe the hurricane devastated the city beyond repair. At the 1% significance level, do the data provide
In the article “Prothrombotic Factors in Children With Stroke or Porencephaly” (Pediatrics Journal, Vol. 116, Issue 2, pp. 447–453), J. Lynch et al. compared differences and similarities in children with arterial ischemic stroke and porencephaly. Three classification categories were used:
In the article “Drowning Deaths of Zero to Five Year Old Children in Victorian Dams, 1989–2001” (Australian Journal of Rural Health, Vol. 13, Issue 5, pp. 300–308), L. Bugeja and R. Franklin examined drowning deaths of young children in Victorian dams to identify common contributing factors
In a Zogby International Poll, conducted in early 2006 in conjunction with Le Moyne College’s Center for Peace and Global Studies, roughly 29% of the 944 military respondents serving in Iraq in various branches of the armed forces said the United States should leave Iraq immediately. Do the data
A recent Harris Interactive survey found that 92.0% of 1001 American adults said they always wash up after using the bathroom. a. At the 5% significance level, do the data provide sufficient evidence to conclude that more than 9 of 10 Americans always wash up after using the bathroom? b. Repeat
A New York Times/CBS News poll asked a sample of U.S. adults whether illegal immigrants who have been in the United States for at least 2 years should be allowed to apply for legal status. Of the 1125 people sampled, 62% replied in the affirmative. At the 1% significance level, do the data provide
In an ABC Global Kids Study, conducted by Roper Starch Worldwide, Inc., estimates were made in various countries of the percentage of children who attend church at least once a week. Two of the countries in the survey were the United States and Germany. Considering these two countries only,a.
Industry Research polled teenagers on sunscreen use. The survey revealed that 46% of teenage girls and 30% of teenage boys regularly use sunscreen before going out in the sun. a. Identify the specified attribute. b. Identify the two populations. c. Are the proportions 0.46 (46%) and 0.30 (30%)
Repeat parts (b)€“(e) of Exercise 11.5 for samples of size 4. (There are five possible samples.)
Consider a hypothesis test for two population proportions with the null hypothesis H0: p1 = p2. What parameter is being estimated by the a. Sample proportion pˆ1? b. Sample proportion pˆ2? c. Pooled sample proportion pˆp?
Of the quantities p1, p2, x1 , x2, pˆ1, pˆ2, and pˆp, a. Which represent parameters and which represent statistics? b. Which are fixed numbers and which are variables?
x1 = 10, n1 = 20, x2 = 18, n2 = 30; left-tailed test, α = 0.10; 80% confidence interval a. Determine the sample proportions. b. Decide whether using the two-proportions z-procedures is appropriate. If so, also do parts (c) and (d). c. Use the two-proportions z-test to conduct the required
x1 = 18, n1 = 40, x2 = 30, n2 = 40; left-tailed test, α = 0.10; 80% confidence interval a. Determine the sample proportions. b. Decide whether using the two-proportions z-procedures is appropriate. If so, also do parts (c) and (d). c. Use the two-proportions z-test to conduct the required
x1 = 14, n1 = 20, x2 = 8, n2 = 20; right-tailed test, α = 0.05; 90% confidence interval a. Determine the sample proportions. b. Decide whether using the two-proportions z-procedures is appropriate. If so, also do parts (c) and (d). c. Use the two-proportions z-test to conduct the required
x1 = 15, n1 = 20, x2 = 18, n2 = 30; right-tailed test, α = 0.05; 90% confidence interval a. Determine the sample proportions. b. Decide whether using the two-proportions z-procedures is appropriate. If so, also do parts (c) and (d). c. Use the two-proportions z-test to conduct the required
x1 = 18, n1 = 30, x2 = 10, n2 = 20; two-tailed test, α = 0.05; 95% confidence interval a. Determine the sample proportions. b. Decide whether using the two-proportions z-procedures is appropriate. If so, also do parts (c) and (d). c. Use the two-proportions z-test to conduct the required
x1 = 30, n1 = 80, x2 = 15, n2 = 20; two-tailed test, α = 0.05; 95% confidence intervala. Determine the sample proportions.b. Decide whether using the two-proportions z-procedures is appropriate. If so, also do parts (c) and (d).c. Use the two-proportions z-test to conduct the required hypothesis
Approximately 450,000 vasectomies are performed each year in the United States. In this surgical procedure for contraception, the tube carrying sperm from the testicles is cut and tied. Several studies have been conducted to analyze the relationship between vasectomies and prostate cancer. The
For several years, evidence had been mounting that folic acid reduces major birth defects. A. Czeizel and I. Dudas of the National Institute of Hygiene in Budapest directed a study that provided the strongest evidence to date. Their results were published in the paper “Prevention of the First
Repeat parts (b)€“(e) of Exercise 11.5 for samples of size
In the paper “The Racial Crossover in Comorbidity, Disability, and Mortality” (Demography, Vol. 37(3), pp. 267–283), N. Johnson investigated the health of independent random samples of white and African-American elderly (aged 70 years or older). Of the 4989 white elderly surveyed, 529 had at
Response Insurance collects data on seatbelt use among U.S. drivers. Of 1000 drivers 25–34 years old, 27% said that they buckle up, whereas 330 of 1100 drivers 45–64 years old said that they did. At the 10% significance level, do the data suggest that there is a difference in seat-belt use
Guns make unique markings on bullets they fire and their shell casings. These markings are called ballistic fingerprints. An ABCNEWS Poll examined the opinions of Americans on the enactment of a law “._______._______. that would require every gun sold in the United States to be test-fired first,
Body mass index (BMI) is a measure of body fat based on height and weight. According to the document Dietary Guidelines for Americans, published by the U.S. Department of Agriculture and the U.S. Department of Health and Human Services, for adults, a BMI of greater than 25 indicates an above
Refer to Exercise 11.88 and determine and interpret a 98% confidence interval for the difference between the prostate cancer rates of men who have had a vasectomy and those who have not. In exercise Approximately 450,000 vasectomies are performed each year in the United States. In this surgical
Refer to Exercise 11.89 and determine and interpret a 98% confidence interval for the difference between the rates of major birth defects for babies born to women who have taken folic acid and those born to women who have not.In exerciseA. Czeizel and I. Dudas of the National Institute of Hygiene
Refer to Exercise 11.90 and find and interpret a 95% confidence interval for the difference between the stroke incidences of white and African-American elderly. In exercise “The Racial Crossover in Comorbidity, Disability, and Mortality” (Demography, Vol. 37(3), pp. 267–283), N. Johnson
Refer to Exercise 11.91 and find and interpret a 90% confidence interval for the difference between the proportions of seat-belt users for drivers in the age groups 25–34 years and 45–64 years.In exerciseResponse Insurance collects data on seatbelt use among U.S. drivers. Of 1000 drivers
Refer to Exercise 11.92 and find and interpret a 98% confidence interval for the difference between the percentages of women and men who favor ballistic fingerprinting. In exercise Guns make unique markings on bullets they fire and their shell casings. These markings are called ballistic
Refer to Exercise 11.93. Body mass index (BMI) is a measure of body fat based on height and weight. According to the document Dietary Guidelines for Americans, published by the U.S. Department of Agriculture and the U.S. Department of Health and Human Services, for adults, a BMI of greater than 25
A Harris Poll was conducted to estimate the proportion of Americans who feel that marijuana should be legalized for medicinal use in patients with cancer and other painful and terminal diseases. Identify the a. Specified attribute. b. Population. c. Population proportion. d. According to the poll,
The National Association of Colleges and Employers sponsors the Graduating Student and Alumni Survey. Part of the survey gauges student optimism in landing a job after graduation. According to one year’s survey results, published in American Demographics, among the 1218 respondents, 733 said that
Refer to Problem 10. a. Find the margin of error for the estimate of p. b. Obtain a sample size that will ensure a margin of error of at most 0.02 for a 95% confidence interval without making a guess for the observed value of pˆ. c. Find a 95% confidence interval for p if, for a sample of the size
In an issue of Parade Magazine, the editors reported on a national survey on law and order. One question asked of the 2512 U.S. adults who took part was whether they believed that juries “almost always” convict the guilty and free the innocent. Only 578 said that they did. At the 5%
In the article “Height and Weight at Various Ages and Risk of Breast Cancer” (Annals of Epidemiology, Vol. 2, pp. 597–609), L. Brinton and C. Swanson discussed the relationship between height and breast cancer. The study, sponsored by the National Cancer Institute, took 5 years and involved
State and local governments often poll their constituents about their views on the economy. In two polls taken approximately 1 year apart, O’Neil Associates asked 600 Maricopa County, Arizona, residents whether they thought the state’s economy would improve over the next 2 years. In the first
Refer to Problem 14. a. Determine a 98% confidence interval for the difference, p1 − p2, between the proportions of Maricopa County residents who thought that the state’s economy would improve over the next 2 years during the time of the first poll and during the time of the second poll. b.
Refer to Problems 14 and 15.a. Take half the length of the confidence interval found in Problem 15(a) to obtain the margin of error for the estimate of the difference between the two population proportions. Interpret your result in words. b. Solve part (a) by applying Formula 11.3 on page 466. c.
In the New York Times article “A Common Police Vest Fails the Bulletproof Test,” E. Lichtblau reported on a U.S. Department of Justice study of 103 bulletproof vests containing a fiber known as Zylon. In ballistics tests, only 4 of these vests produced acceptable safety outcomes (and resulted
The NCAA Men’s Division I Basketball Championship is held each spring and features 65 college basketball teams. This 20-day tournament is colloquially known as “March Madness.” A Harris Poll asked 2435 randomly selected U.S. adults whether they would participate in an office pool for March
In a Harris Poll of 1961 randomly selected U.S. adults, 1137 said that they do not believe that abstinence programs are effective in reducing or preventing AIDS. At the 5% significance level, do the data provide sufficient evidence to conclude that a majority of all U.S. adults feel that way?
N. Hill et al. conducted a clinical study to compare the standard treatment for head lice infestation with the Bug Buster kit, which involves using a fine-toothed comb on thoroughly wet hair four times at 4-day intervals. The researchers published their findings in the paper “Single Blind,
The Influence of Finasteride on the Development of Prostate Cancer” (New England Journal of Medicine, Vol. 349, No. 3, pp. 215–224), I. Thompson et al. reported the results of a major study to examine the effect of finasteride in reducing the risk of prostate cancer. The study, known as the
a. Use the data from the Gallup poll to determine and interpret a 95% confidence interval for the percentage of all U.S. adults who think that it is the responsibility of the federal government to make sure all Americans have health care coverage. b. Find and interpret the margin of error for the
Explain what each phrase means in the context of inferences for a population proportion. a. Number of successes b. Number of failures
Fill in the blanks. a. The mean of all possible sample proportions is equal to the_______. b. For large samples, the possible sample proportions have approximately a distribution. c. A rule of thumb for using a normal distribution to approximate the distribution of all possible sample
What does the margin of error for the estimate of a population proportion tell you?
A poll was conducted by Opinion Research Corporation to estimate the proportions of men and women who get the “holiday blues.” Identify the a. Specified attribute. b. Two populations. c. Two population proportions. d. Two sample proportions. e. According to the poll, 34% of men and 44% of women
Suppose that you are using independent samples to compare two population proportions. Fill in the blanks. a. The mean of all possible differences between the two sample proportions equals the_______.b. For large samples, the possible differences between the two sample proportions have approximately
Suppose that you want to find a 95% confidence interval based on independent samples for the difference between two population proportions and that you want a margin of error of at most 0.01. a. Without making an educated guess for the observed sample proportions, find the required common sample
Explain how you would use Table V to find the two χ2-values that divide the area under a χ2-curve into a middle 0.95 area and two outside 0.025 areas. Find these two χ2-values for a χ2-curve with df = 14.
It can be shown that the square of a standard normal variable has the chi-square distribution with one degree of freedom. Use that fact to show, for a chi-square curve with one degree of freedom, that χ2 α = z2 α/2.
Use Exercises 12.99 and 12.100 to show that the chisquare homogeneity test for comparing two population proportions and the two-tailed two-proportions z-test are equivalent.
According to Current Housing Reports, published by the U.S. Census Bureau, the primary heating fuel for all occupied housing units is distributed as follows.Suppose that you want to determine whether the distribution of primary heating fuel for occupied housing units built after 2000 differs from
Distribution: 0.2, 0.4, 0.3, 0.1;Observed frequencies: 39, 78, 64, 19;Significance level = 0.05We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at
Distribution: 0.2, 0.4, 0.3, 0.1;Observed frequencies: 85, 215, 130, 70;Significance level = 0.05We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at
Distribution: 0.2, 0.1, 0.1, 0.3, 0.3;Observed frequencies: 29, 13, 5, 25, 28;Significance level = 0.10We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to
Distribution: 0.2, 0.1, 0.1, 0.3, 0.3;Observed frequencies: 9, 7, 1, 12, 21;Significance level = 0.10We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide,
Distribution: 0.5, 0.3, 0.2;Observed frequencies: 45, 39, 16;Significance level = 0.01We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the
Distribution: 0.5, 0.3, 0.2;Observed frequencies: 147, 115, 88;Significance level = 0.01We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the
According to the U.S. Census Bureau publication Demographic Profiles, a relative-frequency distribution of the U.S. resident population by region in 2000 was as follows.A simple random sample of this year's U.S. residents gave the following frequency distribution. align="center">a. Identity the
The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views as liberal, 51.9% as moderate, and 20.4% as
The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and J. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggressive driving and road rage. Road rage is
Observing that the proportion of blue M&Ms in his bowl of candy appeared to be less than that of the other colors, R. Fricker, Jr., decided to compare the color distribution in randomly chosen bags of M&Ms to the theoretical distribution reported by M&M/MARS consumer affairs. Fricker
Consider two χ2-curves with degrees of freedom 12 and 20, respectively. Which one more closely resembles a normal curve? Explain your answer.
An American roulette wheel contains 18 red numbers, 18 black numbers, and 2 green numbers.The following table shows the frequency with which the ball landed on each color in 200 trials.At the 5% significance level, do the data suggest that the wheel is out of balance?
A gambler thinks a die may be loaded, that is, that the six numbers are not equally likely. To test his suspicion, he rolled the die 150 times and obtained the data shown in the following table.Do the data provide sufficient evidence to conclude that the die is loaded? Perform the hypothesis test
The Japan Automobile Manufacturer's Association provides data on exported vehicles in Japan's Motor Vehicle Statistics, Total Exports by Year. In 2005, cars, trucks, and buses constituted 86.4%, 12.1%, and 1.5% of vehicle exports, respectively. This year, a simple random sample of 750 vehicle
The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919- 1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. If two teams are evenly matched, the probabilities of the series
According to market research by Brittain Associates, published in an issue of American Demographics, the income distribution of adult Internet users closely mirrors that of credit card applicants. That is exactly what many major credit card issuers want to hear because they hope to replace direct
In the article "Waves of Rural Brides: Female Marriage Migration in China" (Annals of the Association of American Geographers, Vol. 88(2), pp. 227-251), C. Fan and Y. Huang reported on the reasons that women in China migrate within the country to new places of residence. The percentages for reasons
Table 12.4 on page 482 showed the calculated sums of the observed frequencies, the expected frequencies, and their differences.Strictly speaking, those sums are not needed. However, they serve as a check for computational errors.a. In general, what common value should the sum of the observed

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