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Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions

Referring to Applied Example 10. 7: a. What null hypothesis is being tested in each of these 13 tests? b. Why are the “t-calculated” and the “t-critical” values the important values? c. Why is it correct to report their absolute values for both t-values in Table 14? d. What decision is
a. Describe how you could select two independent samples from among your classmates to compare the heights of female and male students. b. Describe how you could select two dependent samples from among your classmates to compare their heights when they entered high school with their heights when
A research project was undertaken to evaluate two focimeters. Each of 20 lenses of varying powers was read once on each focimeter. The measurement differences were then calculated, where each difference was Focimeter A €“ Focimeter B. Assume readings are normally distributed.a. Using a
Two independent random samples resulted in the following:Find the estimate for the standard error for the difference between two means.
Two independent random samples resulted in the following: Sample A: nA = 24 sA = 8.5 Sample B: nB = 21 sB = 11.3 Find the estimate for the standard error for the difference between two means.
Two independent random samples of sizes 18 and 24 were obtained to make inferences about the difference between two means.What is the number of degrees of freedom? Discuss both cases.
Find the confidence coefficient that would be used to find the maximum error for each of the following situations when estimating the difference between two means m 1 - m2
Find the 90% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations.
A study comparing attitudes toward death was conducted in which organ donors (individuals who had signed organ donor cards) were compared with nondonors. The study is reported in the journal Death Studies. Templer€™s Death Anxiety Scale (DAS) was administered to both groups. On this
The article €œCar rental prices can change in a heartbeat€ (USA Today, March 14, 2007) reported that rates for car rentals can change many times during a day. The national average rate for the January€“March quarter of 2007 was $52.71, yet in some cities, car rentals
Women on average have 8 more pairs of shoes than men, according to a USA Today Snapshot titled €œWho owns more shoes?€ (July 8, 2009). A recent study at a community college gave the following results:a. Find the 90% confidence interval for the difference between the two mean
€œIs the length of a steel bar affected by the heat treatment technique used?€ This was the question being tested when the following data were collected.a. Find the means and standard deviations for the two sets of data. b. Find evidence about the sample data (both graphic and
Approximately 95% of the sunflowers raised in the United States are grown in the states of North Dakota, South Dakota, and Minnesota. To compare yield rates between North and South Dakota, 11 sunflower-producing counties were randomly selected from North Dakota and 14 sunflower-producing counties
At a large university, a mathematics placement exam is administered to all students. Samples of 36 male and 30 female students are randomly selected from this year€™s student body and the following scores recorded:a. Describe each set of data with a histogram (use the same class intervals
State the null and alternative hypotheses that would be used to test the following claims: a. There is a difference between the mean age of employees at two different large companies. b. The mean of population 1 is greater than the mean of population 2. c. The mean yield of sunflower seeds per
State the null and alternative hypotheses that would be used to test the following claims: a. The difference between the means of the two populations is more than 20 lb. b. The mean of population A is less than 50 more than the mean of population B. c. The difference between the two populations
Calculate the estimate for the standard error of difference between two independent means for each of the following cases:
Find the value of t for the difference between two means based on an assumption of normality and this information about two samples:
Find the value of defference two means based on assumption of normality and this information about two samples
Determine the p-value for the following hypothesis tests for the difference between two means with population variances unknown.
Determine the critical values that would be used for the following hypothesis tests (using the classical approach) about the difference between two means with population variances unknown.
For the hypothesis test involving Ha: m B = m A 0, with df = 18 and t = 1.3: a. Find the p-value. b. Find the critical values given a = 0.05.
Suppose the calculated t had been 1.80 in Example 10. 10 (pp. 500–501). Using df = 9 or using df = 20 results in different answers. Explain how the word conservative (p. 496) applies here.
Is having a long, more complex first name more dignified for a girl? Are girls€™ names longer than boys€™ names? With current names like €œAlexandra,€ €œMadeleine,€ and €œSavannah,€ it certainly appears so. To test
Lauren, a brunette, was tired of hearing, €œBlondes have more fun.€ She set out to €œprove€ that €œbrunettes are more intelligent.€ Lauren randomly (as best she could) selected 40 blondes and 40 brunettes at her high school. The
One could reason that high school seniors would have more money issues than high school juniors. Seniors foresee expenses for college as well as their senior trip and prom. So does this mean that they work more than their junior classmates? Christine, a senior at HFL High School, randomly collected
The computer age has allowed teachers to use electronic tutorials to motivate their students to learn. Issues in Accounting Education published the results of a study that showed that an electronic tutorial, along with intentionally induced peer pressure, was effective in enhancing preclass
In a typical month, men spend $178 and women spend $96 on leisure activities,” according to the results of an International Communications Research (ICR) for American Express poll, as reported in a USA Today Snapshot found on the Internet June 25, 2005. Suppose random samples were taken from the
Many cheeses are produced in the shape of a wheel, and due to manufacturing inconsistencies, the amount of cheese, measured by weight, varies from wheel to wheel. Heidi Cembert wishes to determine if there is a significant difference, at the 10% level, between the weight per wheel of Gouda and Brie
If a random sample of 18 homes south of Center Street in Provo has a mean selling price of $145,200 and a standard deviation of $4700, and a random sample of 18 homes north of Center Street has a mean selling price of $148,600 and a standard deviation of $5800, can you conclude that there is a
MINITAB was used to complete a t-test of the difference between two means using the following two independent samples.a. Assuming normality, verify the results (two sample means and standard deviations, and the calculated t) by calculating the values yoursel f. b. Use Table 7 in Appendix B to
Are females as serious about golf as men are? If so, would the price of a driver for a man be the same as the price of a driver for a female? It was contended that women€™s drivers would be cheaper. Random samples of drivers were taken from the Golflink.com website.The prices were:At the
Twenty laboratory mice were randomly divided into two groups of10. Each group was fed according to a prescribed diet.At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet B was greater than
Many people who are involved with Major League Baseball believe that Yankees€™ baseball games tend to last longer than games played by other teams. In order to test this theory, one other MLB team, the St. Louis Cardinals, was picked at random.The time of the game (in minutes) for 12
Penfield and Perinton are two adjacent eastside suburbs of Rochester, New York.They have both always been considered on equal ground with respect to quality of life, housing, and education. Although many new housing developments are going up in Penfield, Perinton offers the added bonus of cheaper
Consider the “commute time” data for college males and females given in Exercise 10.. a. Are the assumptions of normality satisfied for each sample? Explain. b. Test the hypothesis that there is no difference between the mean commute times for male and female college students. Use a 0.05
When evaluating different measuring instruments, one must first determine whether there is a systematic difference between the instruments. Lenses from two different groups (1 and 2) were measured once each by two different instruments.The measurement differences (Instrument A €“
Consider the “surface height” data for Raul’s unpolished and polished reflective surfaces of a silicone microchip given in Applied Example 10. 11 on page 504. a. Present and describe each set of data (unpolished and polished) using a histogram, the mean, and the standard deviation. b. Check
Consider the “surface height” data for Raul’s unpolished and polished reflective surfaces of a silicone microchip given in Applied Example 10. 11 on page 504 and initially investigated in Exercise 10. 77. a. Do the two sets of data, unpolished and polished, represent independent or dependent
a. To get acquainted with the two theoretical populations, randomly select a very large sample from each. Generate 2000 data values, calculate mean and standard deviation, and construct a histogram using class boundaries that are multiples of one-half of a standard deviation (10) starting at the
One reason for being conservative when determining the number of degrees of freedom to use with the tdistribution is the possibility that the population variances might be unequal. Extremely different values cause a lowering in the number of df used. Repeat Exercise 10. 79 using theoretical normal
Unbalanced sample sizes are a factor in determining the number of degrees of freedom for inferences about the difference between two means. Repeat Exercise 10. 79 using theoretical normal distributions of N(100, 20) and N(120, 20) and sample sizes of 5 and 20. Check all three properties of the
One assumption for the two-sample t-test is that the “sampled populations are to be normally distributed.” What happens when they are not normally distributed? Repeat Exercise 10. 79 using two theoretical populations that are not normal and using samples of size 10. The exponential distribution
Only 75 of the 250 people interviewed were able to name the vice president of the United States. Find the values for x, n, p, and q.
If n1 = 40 p1 = 0.9 n2 = 50 and p2 = 0.9 a. Find the estimated values for both np’s and both nq’s. b. Would this situation satisfy the guidelines for approximately normal? Explain.
Calculate the estimate for the standard error of the difference between two proportions for each of the following cases:
Calculate the maximum error of estimate for a 90% confidence interval for the difference between two proportions for the following cases:
A Nursing Economics article titled €œNurse Executive Turnover€ compared two groups of nurse executives. One group had participated in a unique program for nurse executives called the Wharton Fellows Program, and the other group had not participated in the program. Of 341
Find the 95% confidence interval for p A = p B.
The proportions of defective parts produced by two machines were compared, and the following data were collected: Machine: 1 n = 150; number of defective parts = 12 Machine 2: n = 150 number of defective parts = 6 Determine a 90% confidence interval for p1 = p2
In a random sample of 40 brown-haired individuals, 22 indicated that they use hair coloring. In another random sample of 40 blond individuals, 26 indicated that they use hair coloring. Use a 92% confidence interval to estimate the difference in the population proportions of brunettes and blondes
The Soap and Detergent Association issued its fifth annual Clean Hands Report Card survey for 2009. From the answers to a series of hygiene-related questions posed to American adults, it was found that 62% of 442 women washed their hands more than 10 times per day, while 37% of 446 men did the
In a survey of 300 people from city A, 128 prefer New Spring soap to all other brands of deodorant soap. In city B, 149 of 400 people prefer New Spring soap. Find the 98% confidence interval for the difference in the proportions of people from the two cities who prefer New Spring soap.
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims: a. There is no difference between the proportions of men and women who will vote for the incumbent in next month’s election. b. The percentage of boys who cut classes is greater than the
Show that the standard error of which isWhen p1 = p2 = p
Find the values of pp and qp for these samples:
Find the value of z that would be used to test the difference between the proportions, given the following:
Find the p-value for the test with alternative Hypothesis Pe< pR using the data in Exercise 10. 95.
Determine the p-value that would be used to test the following hypotheses when z is used as the test statistic
Determine the critical region and critical value(s) that would be used to test (classical procedure) the following hypotheses when z is used as the test statistic.
Referring to the sample of 200 adults surveyed in Section 11. 1’s Cooling a Great Hot Taste a. What information was collected from each adult in the sample? b. Define the population and the variable involved in the sample. c. Using the sample data, calculate percentages for the various methods
State the null hypothesis Ho and the alternative hypothesis Ha that would be used to test the following statements. a. The four choices are all equally likely. b. The poll showed the political party distributions of 23%, 36%, and 41% for Republicans, Democrats, and Independents, respectively. c.
Determine the p-value for the following hypotheses tests involving the x2-distribution.
Determine the critical value and critical region that would be used in the classical approach to test the null hypothesis for each of the following multinomial experiments.a. Ho: P(1) = P(2) = P(3) = P(4) = 0.25, with a = 0.05b. Ho: P(I) = 0.25, P(II) = 0.40, P(III) = 0.35 with Explain how
Explain how 312.75, 2.25, and 0.0162 were obtained in the first row of Table 11. 4
A manufacturer of floor polish conducted a consumer-preference experiment to determine which of five different floor polishes was the most appealing in appearance. A sample of 100 consumers viewed five patches of flooring that had each received one of the five polishes. Each consumer indicated the
Skittles Original Fruit bite-size candies are multiple-colored candies in a bag, and you can €œTaste the Rainbow€ with their five colors and flavors: green€”lime, purple€”grape, yellow€”lemon, orange€”orange, red€” strawberry.
An October 16, 2009, USA Today Snapshot titled “Are public cell phone conversations rude?” reported the following results from a Fox TV/Rasmussen Reports poll: Poll Response Percent Yes.......... 51 No .......... 37 Not sure.......... 12 As a member of the Civility Committee at your
National health care is currently a big issue for Americans. The October 21, 2009, USA Today article €œPoll: Americans skittish over health care changes€ reported the following percentages with respect to €œInsurance company requirements you have to meet to get
A certain type of flower seed will produce magenta, chartreuse, and ochre flowers in the ratio 6_3_1 (one flower per seed). A total of 100 seeds are planted and all germinate, yielding the following results.Solve the following using the p-value approach and the classical approach: a. If the null
Referring to the sample of 200 adults surveyed in Section 11. 1’s Cooling a Great Hot Taste and the accompanying “Putting Out the Fire” graphic: a. How do the sample percentages calculated in part c of Exercise 11. 1 compare to the percentages on the “Putting Out the Fire” graphic? b.
Bird foraging behavior is being studied in a managed forest that is made up of Douglas fir (52% of canopy volume), ponderosa pine (36%), and grand fir (12%).Two hundred thirty-eight red-breasted nuthatches were observed, with 105 in Douglas fir, 92 in ponderosa pine, and 41 in grand fir. The null
A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.10, 0.30, 0.35, and 0.25, respectively, from the least to most expensive variety. A sample of 500 purchases resulted in sales of 46, 162, 191, and 101 of the
One of the major benefits of e-mail is that it makes it possible to communicate rapidly without getting a busy signal or no answer, two major criticisms of telephone calls. But does e-mail succeed in helping solve the problems people have trying to run computer software? A study polled the opinions
Nursing Magazine reported results of a survey of more than 1800 nurses across the country concerning job satisfaction and retention. Nurses from magnet hospitals (hospitals that successfully attract and retain nurses) describe the staffing situation in their units as follows:A survey of 500 nurses
A program for generating random numbers on a computer is to be tested. The program is instructed to generate 100 single-digit integers between 0 and 9. The frequencies of the observed integers are as follows:At the 0.05 level of significance, is there sufficient reason to believe that the integers
€œClimbing out of debt, step by step,€ an article in the April 29, 2005, USA Today, reported results of a survey of 260 members of the Financial Planning Association. Financial planners each reported what he or she considers to be the one most valuable step people can take to
The U.S. census found that babies enter the world on the days of the week in the proportions that follow.A random sample selected from the birth records for a large metropolitan area resulted in the following data: a. Do these data provide sufficient evidence to reject the claim €œBirths
Referring to the sample of 200 adults surveyed in Section 11.1’s Cooling a Great Hot Taste and the accompanying “Putting Out the Fire” graphic: Does the sample of 200 adults show a distribution that is significantly different from the distribution shown in the “Putting Out the Fire”
To demonstrate/explore the effect increased sample size has on the calculated chi-square value, let€™s consider the Skittles candies in Exercise 11.16 and sample some larger bags of the candy.a. Suppose we purchase a 16-oz bag of Skittles, count the colors, and observe exactly the same
According to The Harris Poll, the proportion of all adults who live in households with rifles (29%), shotguns (29%), or pistols (23%) has not changed significantly. However, today more people live in households with no guns (61%).The 1014 adults surveyed gave the following results.In a survey of
Using Table 8 of Appendix B, find the following: a. x2(10, 0.01) b. x2(12, 0.025) c. x2(10, 0.95) d. x2(22, 0.995)
Why is the chi-square test typically a one-tail test with the critical region in the right tail? a. What kind of value would result if the observed frequencies and the expected frequencies were very close in value? Explain how you would interpret this situation. b. Suppose you had to roll a die 60
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. The voters expressed preferences that were not independent of their party affiliations. b. The distribution of opinions is the same for all three communities. c. The proportion
The “test of independence” and the “test of homogeneity” are completed in identical fashion, using the contingency table to display and organize the calculations. Explain how these two hypothesis tests differ.
Find the expected value for the cell shown.
Identify these values from Table 11. 7: a. C2 b. R1 c. n d. E2,3
MINITAB was used to complete a chi-square test of independence between the number of boat-related manatee deaths and two Florida counties.Chi-Square Test: Boat-Related Deaths, Non-Boat- Related Deaths Expected counts are printed below observed counts Chi-Square contributions are printed below
Results on seatbelt usage from the 2003 Youth Risk Behavior Survey were published in a USA Today Snapshot on January 13, 2005. The following table outlines the results from the high school students who were surveyed in the state of Nebraska. They were asked whether they rarely or never wear
The State Conservation Department used surveillance cameras to study the reaction of white-tailed deer to traffic as they used a wildlife underpass to cross a major highway. When a car or truck passed over while the deer were in the underpass, they recorded €œcontinued€ when
A survey of randomly selected travelers who visited the service station restrooms of a large U.S. petroleum distributor showed the following results:Using a = 0.05 does the sample present sufficient evidence to reject the hypothesis €œQuality of responses is independent of the gender of
Tourette€™s syndrome is an inheritable, childhood onset neurological disorder involving multiple motor tics and at least one vocal tic. A U.S. study that was published in the June 5, 2009, CDC Morbidity and Mortality Weekly Report indicated that the syndrome occurs in 3 out of every 1000
Find these critical values by using Table 8 of Appendix B. a. x2(18, 0.01) b. x2(16, 0.025) c. x2(40, 0.10) d. x2(45, 0.01)
Tourette€™s syndrome is an inheritable, child hood onset neurological disorder involving multiple motor tics and at least one vocal tic. A U.S. study that was published in the June 5, 2009, CDC Morbidity and Mortality Weekly Report indicated that the syndrome occurs in 3 out of every 1000
A survey of employees at an insurance firm concerned worker€“supervisor relationships. One statement for evaluation was, €œI am not sure what my supervisor expects.€ The results of the survey are presented in the following contingency table.Can we reject the
a. Solve using the p-value approach.b. Solve using the classical approach.
A random sample of 500 married men was taken; each person was cross-classified as to the size community that he was presently residing in and the size community that he was reared in. The results are shown in the following table.Does this sample contradict the claim of independence, at the 0.01
It is hypothesized that sick animals receiving a certain drug (the treated group) will survive at a more favorable rate than those that do not receive the drug (the control group).The following results were recorded from the test.a. Explain why the hypothesis stated in the exercise cannot be the
The manager of an assembly process wants to determine whether or not the number of defective articles manufactured depends on the day of the week the articles are produced. She collected the following information.Is there sufficient evidence to reject the hypothesis that the number of defective
Referring to Applied Example 11. 7: a. Express the percentage of Americans who “prefer baked” to “other” by region as a 2 = 4 contingency table. b. Explain why the following question could be tested using the chi-square statistic: “Is the preference for baked the same in all four regions

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