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

You are interested in comparing the null hypothesis p = 0.8 against the alternative hypothesis p = 0.8. In 100 trials you observe 73 successes. Calculate the p-value associated with this result.
The Kaiser Family Foundation conducted a national survey in 2003 of 17,685 seniors. The purpose of the survey was to capture detailed information about seniors’ prescription drug use, coverage, and experiences a. If this were a random sample that satisfied all the requirements for an inference
The Pizza Shack has been experimenting with different recipes for their pizza crust, thinking they might replace their current recipe. They are planning to sample pizza made with the new crust. Before sampling, a strategy is needed so that after the tasting results are in, Pizza Shack will know how
The Pizza Shack in Exercise 9.177 has completed its sampling and the results are in! On Tuesday afternoon, they sampled 15 customers and 9 preferred the new pizza crust. On Friday evening, they sampled 200 customers and 120 preferred the new pizza crust. Help the manager interpret the meaning of
The owner of the Pizza Shack in Exercises 9.177 and 9.178 does not understand the use of the normal distribution and z in Exercise 9.178. Help the manager interpret the meaning of the results by redoing both hypothesis tests using x = number of customers preferring the new crust as the test
Use a computer or calculator to find the area to the right of t = 1.12 with df = 15 Draw a sketch showing the question with the answer.
An instructor asks each of the 54 members of his class to write down “at random” one of the numbers 1, 2, 3, . . . , 13, 14, 15. Since the instructor believes that students like gambling, he considers 7 and 11 to be lucky numbers. He counts the number of students, x, who selected 7 or 11. How
Today’s newspapers and magazines often report the findings of survey polls about various aspects of life. The Pew Internet & American Life Project (January 13–February 9, 2005) found that “63% of cell phone users ages 18-27 have used text messaging within the past month.” Other information
To test the hypothesis that the standard deviation on a standard test is 12, a sample of 40 randomly selected students’ exams was tested. The sample variance was found to be 155. Does this sample provide sufficient evidence to show that the standard deviation differs from 12 at the 0.05 level of
Bright-Lite claims that its 60-watt light bulb burns with a length of life that is approximately normally distributed with a standard deviation of 81 hours. A sample of 101 bulbs had a variance of 8075. Is this sufficient evidence to reject Bright-Lite’s claim in favor of the alternative,“the
A production process is considered out of control if the produced parts have a mean length different from 27.5 mm or a standard deviation that is greater than 0.5 mm. A sample of 30 parts yields a sample mean of 27.63 mm and a sample standard deviation of 0.87 mm. If we assume part length is a
Julia Jackson operates a franchised restaurant that specializes in soft ice cream cones and sundaes. Recently she received a letter from corporate headquarters warning her that her shop is in danger of losing its franchise because the average sales per customer have dropped “substantially below
All tomatoes that a certain supermarket buys from growers must meet the store’s specifications of a mean diameter of 6.0 cm and a standard deviation of no more than 0.2 cm. The supermarket’s buyer visits a potential new supplier and selects a random sample of 36 tomatoes from the grower’s
The uniform length of nails is very important to a carpenter—the length of the nails being used are matched to the materials being fastened together, thereby making a small standard deviation an important property of the nails. A sample of 35 randomly selected 2-inch nails is taken from a large
It is important that the force required to extract a cork from a wine bottle not have a large standard deviation. Years of production and testing indicate that the no. 9 corks in Applied Example 6.13 (p. 285) have an extraction force that is normally distributed with a standard deviation of 36
A box of Corn Flakes that is labeled €œNET WT. 14 OZ.€ should have 14 oz or more of cereal inside. Twenty of these boxes were randomly selected and the weight of the contents (in ounces) determined.a. Draw a histogram of the weight of cereal per box. b. Find the sample
a. State two ways in which the standard normal distribution and Student’s t-distribution are alike. b. State two ways in which they are different.
The manager in Exercise 9.189 believes that the cereal-filling machine used for Corn Flakes needs to be replaced and that the new one he is considering will pay for the upgrade within a short time, mainly due to less variability in the fill amount. The new machine is started, and a test run is
The boxes of Corn Flakes in Exercises 9.189 and 9.190 that have more than 14.2 oz of cereal are being considered “too full.” Since the weights appear to be normally distributed for both filling machines, use the normal distribution and find the following information for the manager. a. What
Consider the sample data in exercise 9.1. a. Find the mean and standard deviation for the “floor-to-door” time. b. How would you estimate the mean “floor-to-door” time for all female college students?
The variance for each of Student’s t-distributions is equal to df/(df - 2) Find the standard deviation for a Student’s t-distribution with each of the following degrees of freedom: a. 10 b. 20 c. 30 In summary: d. Explain how this verifies Property 5 of the t-distributions listed on page
Construct a 95% confidence interval estimate for the mean µ using the sample information n = 24 = 16.7 and s = 2.6
Construct a 90% confidence interval estimate for the mean µ using the sample information n = 53 = 87.2 and s = 11.9.
The National Highway Traffic Safety Administration found the U.S. average EMS response time from EMS notification to arrival at the crash scene in urban areas to be 6.85 minutes. A random sample of 20 reported fatal crashes in South Dakota had a mean notification-to arrival time of 5.25 minutes
Based on a survey of 1000 adults by Greenfield Online and reported in a May 2009 USA Today Snapshot, adults 24 years of age and under spend a weekly average of $35 on fast food. If 200 of the 1000 adults surveyed who were in the 24 and under age category provided a standard deviation of $14.50,
The Robertson square drive screw was invented in 1908, but it has gained in popularity with American woodworkers and home craftspeople only within the last 10 years. The advantages of square drives over conventional screws is indeed remarkable—most notably greater strength, increased holding
While writing an article on the high cost of college education, a reporter took a random sample of the cost of new textbooks for a semester. The random variable x is the cost of one book. Her sample data can be summarized by n = 41 ∑x = 3582.17 and ∑(x - x)2 = 9960.336 a. Find the sample
Using the computer output in Exercise 9.27, determine the value for each of the following: a. Point estimate b. Confidence coefficient c. Standard error of the mean d. Maximum error of estimate, E e. Lower confidence limit f. Upper confidence limit
The addition of a new accelerator is claimed to decrease the drying time of latex paint by more than 4%. Several test samples were conducted with the following percentage decrease in drying time.Assume that the percentage decrease in drying time is normally distributed. a. Find the 95% confidence
Make a list of four numbers that total “zero.” How many numbers were you able to pick without restriction? Explain how this demonstrates degrees of freedom.
Use a computer or calculator to construct a 0.98 confidence interval using the sample data:
Lunch breaks are often considered too short, and employees frequently develop a habit of €œstretching€ them.The manager at Giant Mart randomly identified 22 employees and observed the lengths of their lunch breaks (in minutes) for one randomly selected day during the week:a.
Many studies have been done telling us that we need to exercise to lower various health risks such as high blood pressure, heart disease, and high cholesterol. But knowing and doing are not the same things. People in the health professions should be even more aware of the need for exercise. The
The fuel economy information on a new SUV€™s window sticker indicates that its new owner can expect 16 mpg (miles per gallon) in city driving and 20 mpg for highway driving and 18 mpg overall. Accurate gasoline records for one such vehicle were kept, and a random sample of mileage per
James Short (1708€“1768), a Scottish optician, constructed the highest-quality reflectors of his time. It was with these reflectors that Short obtained the following measurements of the parallax of the sun (in seconds of a degree), based on the 1761 transit of Venus. The parallax of the
State the null hypothesis, Ho, and the alternative hypothesis,Ha, that would be used to test each of the following claims: a. The mean weight of honeybees is at least 11 grams. b. The mean age of patients at Memorial Hospital is no more than 54 years. c. The mean amount of salt in granola snack
State the null hypothesis, Ho, and the alternative hypothesis,Ha, that would be used to test each of the following claims: a. A chicken farmer at Best Broilers claims that his chickens have a mean weight of 56 oz. b. The mean age of U.S. commercial jets is less than 18 years. c. The mean monthly
Calculate the value of t_ for the hypothesis test: Ho: µ = 32 Ha: µ > 32 n = 16 = 32.93 s = 3.1
Calculate the value of t for the following hypothesis test: Ho: µ = 73 Ha: µ = 73 n = 12 = 71.46 s = 4.1.
Determine the p-value for the following hypothesis tests involving Student€™s t-distribution with 10 degrees of freedom.
Explain the relationship between the critical values found in the bottom row of Table 6 and the critical values of z given in Table 4A.
Determine the critical region and critical value(s) that would be used in the classical approach to test the following null hypotheses:
a. Find the value of P and state the decision for the hypothesis test in Exercise 9.37 using a = 0.05 b. Find the critical region and critical value and state the decision for the hypothesis test in Exercise 9.37 using a = 0.05.
a. Use Table 6 or Table 7 in Appendix B to find the value of P for the hypothesis test in Exercise 9.38; state the decision using a = 0.05 b. Find the critical region and critical values for the hypothesis test in Exercise 9.38; state the decision using a = 0.05
Use a computer or calculator to find the p-value for the following hypothesis test: Ho: µ = 32 Ha: m_32 n = 16 x = 32.93 s = 3.1
Use a computer or calculator to find the p-value for the following hypothesis test: Ho: µ = 73 Ha: µ = 73, n = 12 x = 71.46 s = 4.1
Use both the p-value and the classical approaches to hypothesis testing to reach a decision for each of the following situations. Use a = 0.05d. Compare the results of the two techniques for each case.
In reference to Applied Example 9.7 (p. 425): a. Verify that t(44) = 1.92 is significant at the 0.05 level. b. Verify that t(44) = 3.41 significant at the 0.01 level. c. Explain why t(44) = 1.81 p < 0.10 makes sense only if the hypothesis test is two-tailed. d. If the test is one-tailed, what
A student group maintains that each day, the average student must travel at least 25 minutes one way to reach the college. The college admissions office obtained a random sample of 31 one-way travel times from students. The sample has a mean of 19.4 minutes and a standard deviation of 9.6 minutes.
Homes in a nearby college town have a mean value of $88,950. It is assumed that homes in the vicinity of the college have a higher mean value. To test this theory, a random sample of 12 homes is chosen from the college area. Their mean valuation is $92,460, and the standard deviation is $5200.
According to the August 2009 Reader’s Digest article “Where Our Garbage Goes,” the average American tosses 4.6 pounds of garbage every day. A small town in Vermont initiated a Going Green campaign and asked residents to work on recycling more and reducing their generation of garbage each day.
Find: a. t(12, 0.01) b. t(22, 0.025) c. t(50, 0.10) d. t(8, 0.005)
Up all night? Caffeine cravings may cause longterm health problems. Homework, jobs, and studying all may be causes for teens to consume too much coffee in their everyday lives. Health officials warn that high caffeine intake is not good for anyone, but coffee drinking continues to become more and
Using the computer output in Exercise 9.51, determine the values of the following terms: a. Hypothesized value of population mean b. Sample mean c. Population standard deviation d. Sample standard deviation e. Test statistic
Use a computer or calculator to complete the hypothesis test Ho: µ = 52 Ha: µ
The recommended number of hours of sleep per night is 8 hours, but everybody €œknows€ that the average college student sleeps less than 7 hours. The number of hours slept last night by 10 randomly selected college students is listed here:Use a computer or calculator to complete
It is claimed that the students at a certain university will score an average of 35 on a given test. Is the claim reasonable if a random sample of test scores from this university yields 33, 42, 38, 37, 30, 42? Complete a hypothesis test using a = 0.05 Assume test results are normally distributed.
Gasoline pumped from a supplier€™s pipeline is supposed to have an octane rating of 87.5. On 13 consecutive days, a sample was taken and analyzed, with the following results.a. If the octane ratings have a normal distribution, is there sufficient evidence to show that these octane
According to statements from the National Women’s Health Information Center and the Centers for Disease Control and Prevention, people should exercise at least 60 minutes per week to lower various health risks. a. Based on the data from Exercise 9.32, determine if the technicians exercise at
Consider the “floor-to-door” scenario on page 412, where a random sample of 81 female American college students were each issued a stopwatch and asked to time themselves as they prepared to attend class on the following Thursday morning. The instructions were to start the watch as soon as their
The density of the earth relative to the density of water is known to be 5.517 g/cm3. Henry Cavendish, an English chemist and physicist (1731€“1810), was the first scientist to accurately measure the density of the earth. Following are 29 measurements taken by Cavendish in 1798 using a
Find these critical values using Table 6 in Appendix B: a. t(25, 0.05) b. t(10, 0.10) c. t(15, 0.01) d. t(21, 0.025)
Use a computer or calculator to complete the calculations and the hypothesis test for this exercise. Delco Products, a division of General Motors, produces commutators designed to be 18.810 mm in overall length. (A commutator is a device used in the electrical system of an automobile.) The
Acetaminophen is an active ingredient found in more than 600 over-the-counter and prescription medicines, such as pain relievers, cough suppressants, and cold medications. It is safe and effective when used correctly, but taking too much can lead to liver damage. Source: www.keepkidshealthy.com/ A
A winemaker has placed a large order for the no. 9 corks described in Applied Example 6.13 (p. 285) and is concerned about the number of corks that might have smaller diameters. During the corking process, the corks are squeezed down to 16 to 17 mm in diameter for insertion into bottles with an 18
Length is not very important in evaluating the quality of corks because it has little to do with the effectiveness of a cork in preserving wine. Winemakers have several lengths to choose from and order the length of cork they prefer (long corks tend to make a louder pop when the bottle is
How important is the assumption "The sampled population is normally distributed" to the use of Student's t-distribution? Using a computer, simulate drawing 100 samples of size 10 from each of three different types of population distributions, namely, a normal, a uniform, and an exponential. First
Of the 150 elements in a random sample, 45 are classified as “success.” a. Explain why x and n are assigned the values 45 and 150, respectively. b. Determine the value of p. Explain how p_ is found and the meaning of p. For each of the following situations, find p. c. x = 24 n = 250 d. x =
a. What is the relationship between p = P(success) and q = P(failure)? Explain. b. Explain why the relationship between p and q can be expressed by the formula q = 1 – p c. If P = 0.6 what is the value of q? d. If the value of q’ = 0.273 what is the value of p?
a. Does it seem reasonable that the mean of the sampling distribution of observed values of p should be p, the true proportion? Explain. b. Explain why p is an unbiased estimator for the population p.
Show that simplifies to
Find a, the area of one tail, and the confidence coefficients of z that are used with each of the following levels of confidence. a. 1 - a = 0.90 b. 1 - a = 0.95 c. 1 - a = 0.99
Find: a. t(18, 0.90) b. t(9, 0.99) c. t(35, 0.975) d. t(14, 0.98)
Find a, the area of one tail, and the confidence coefficients of z that are used with each of the following levels of confidence. a. 1 - a = 0.80 b. 1 - a = 0.98 c. 1 - a = 0.75
Refer back to Example 9.8, page 436. Another sample is taken to estimate the proportion of convertibles. Results are n = 400 and x = 92 Find: a. the estimate for the standard error. b. the 95% confidence interval.
“You say tomato, burger lovers say ketchup!” According to a recent T.G.I. Friday’s restaurants’ random survey of 1027 Americans, approximately half (47%) said that ketchup is their preferred burger condiment. The survey quoted a margin of error of plus or minus 3.1%. a. Describe how this
Although most people are aware of minor dehydration symptoms such as dry skin and headaches, many are less knowledgeable about the causes of dehydration. According to a poll done for the Nutrition Information Center, the results of a random sample of 3003 American adults showed that 20% did not
A bank randomly selected 250 checking account customers and found that 110 of them also had savings accounts at the same bank. Construct a 95% confidence interval for the true proportion of checking account customers who also have savings accounts.
In a sample of 60 randomly selected students, only 22 favored the amount budgeted for next year’s intramural and interscholastic sports. Construct the 99% confidence interval for the proportion of all students who support the proposed budget amount.
The National Highway Traffic Safety Administration found that, among the crashes with recorded times, EMS notification times exceeded 10 minutes in 19.4% of rural fatal crashes. A random sample of 500 reported fatal crashes in Kentucky showed 21.8% of the notification times exceeded 10 minutes.
In a poll conducted by Harris Interactive of 1179 video-gaming U.S. youngsters, 8.5% displayed behavioral signs that may indicate addiction. Using a 99% confidence interval for the true binomial proportion based on this random sample of 1179 binomial trials and an observed proportion of 0.085,
Just one serving a month of kale or collard greens or more than two servings of carrots a week can reduce the risk of glaucoma by more than 60%, according to a UCLA study of 1000 women. Using a 90% confidence interval for the true binomial proportion based on this random sample of 1000 binomial
Find these critical values using Table 6 in Appendix B: a. t(21, 0.95) b. t(26, 0.975) c. t(27, 0.99) d. t(60, 0.025)
Using the MINITAB output and information in Exercise 9.79, determine the values of the following terms: a. Point estimate b. Confidence coefficient c. Standard error of the mean d. Maximum error of estimate, E e. Lower confidence limit f. Upper confidence limit
A Cambridge Consumer Credit Index nationwide telephone survey of 1000 people found that most Americans are not easily swayed by the lure of reward points or rebates when deciding to use a credit card or pay by cash or check. The survey found that 2 out of 3 consumers do not even have credit cards
Construct 90% confidence intervals for the binomial parameter p for each of the following pairs of values. Write your answers on the chart.f. Explain the relationship between the answers to parts a and b. g. Explain the relationship among the answers to parts c€“e.
Three nationwide poll results are described below. Each of the polls is based on approximately 1005 randomly selected adults. a. Calculate the 95% confidence maximum error of estimate for the true binomial proportion based on binomial experiments with the same sample size and observed proportion
a. If x successes result from a binomial experiment with n = 1000 and p = P(success) and the 95% confidence interval for the true probability of success is determined, what is the maximum value possible for the “maximum error of estimate”? b. Compare the numerical value of the “maximum error
Karl Pearson once tossed a coin 24,000 times and recorded 12,012 heads.a. Calculate the point estimate for p = P(head) based on Pearson€™s results.b. Determine the standard error of proportion.c. Determine the 95% confidence interval estimate for p = P(head)d. It must have taken Mr.
When a single die is rolled, the probability of a one is 1/6, or 0.167. Let’s simulate 3000 rolls of a die. a. Use the commands given in Exercise 9.85 and a calculator or computer to simulate the rolling of a single die 3000 times. Using the results from the simulation: b. Sum the data and
The “rule of thumb” stated on page 434 indicated that we would expect the sampling distribution of p_ to be approximately normal when “n = 20 and both np and nq are greater than 5.”What happens when these guidelines are not followed? a. Use the following set of computer or calculator
Has the law requiring bike helmet use failed? Yankelovich Partners conducted a survey of bicycle riders in the United States. Only 60% of the nationally representative sample of 1020 bike riders reported owning a bike helmet. a. Find the 95% confidence interval for the true proportion p for a
Find the sample size n needed for a 95% interval estimate in Example
Using the notation of Exercise 9.8, name and find the following critical values of t:
Find n for a 90% confidence interval for p with E = 0.02 using an estimate of p = 0.25
According to a May 2009 Harris Poll, 72% of those who drive and own cell phones say they use them to talk while they are driving. You wish to conduct a survey in your city to determine what percent of the drivers with cell phones use them to talk while driving. Use the national figure of 72% for
Lung cancer is the leading cause of cancer deaths in both women and men in the United States. According to Centers for Disease Control and Prevention 2005 statistics, lung cancer accounts for more deaths than breast cancer, prostate cancer, and colon cancer combined. Overall, only about 16% of all
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims: a. More than 60% of all students at our college work part-time jobs during the academic year. b. No more than one-third of cigarette smokers are interested in quitting. c. A majority of
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims: a. The probability of our team winning tonight is less than 0.50. b. At least 50% of all parents believe in spanking their children when appropriate. c. At most, 80% of the invited guests
Calculate the test statistic z used in testing the following: a. Ho: p = 0.70 Ha: p > 0.70 with the sample n = 300 and x = 224 b. Ho: p = 0.50 Ha: p < 0.50 with the sample n = 450 and x = 207 c. Ho: p = 0.35 vs Ha: p ≠0.35 with the sample n = 280 and x = 94 d. Ho: p = 0.90 vs. Ha: p_0.90

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