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Introductory Statistics 10th Edition Neil A. Weiss - Solutions

The U.S. Department of Justice, Office of Justice Programs, Bureau of Justice Statistics provides information on prison sentences in the document National Corrections Reporting Program. A random sample of 20 maximum sentences for murder yielded the data, in months, presented on the Weiss Stats
The following figure shows the standard normal curve and two t-curves. Which of the two t-curves has the larger degrees of freedom? Explain your answer.
Researchers M. Dhami et al. discussed how people adjust to prison life in the article "Adaption to Imprisonment" (Criminal Justice and Behavior, Vol. 34, No. 8, pp. 1085-1100). A sample of 712 federally sentenced adult male prisoners had an average sentence of 9.15 years. Assume that, for federally
Wildfires are uncontrolled fires that usually spread quickly and are common in wilderness areas that have long and dry summers. The National Interagency Fire Center reports statistics on wildfires on their website www.nifc.gov. The following data lists the size, in thousands of acres, of a sample
Suppose that you have obtained a sample with the intent of performing a particular statistical-inference procedure. What should you do before applying the procedure to the sample data? Why?
At the beginning of this chapter, on page 332, we presented summary statistics for data on bank robberies for five variables: amount stolen, number of bank staff present, number of customers present, number of bank raiders, and travel time from the bank to the nearest police station. These summary
Fill in the following blanks. a. The t-test is ________ to moderate violations of the normality assumption. b. The t-test can sometimes be unduly affected by outliers because the sample mean and sample standard deviation are not ________ to outliers.
In 2011, the average car in the United States was driven 13.5 thousand miles, as reported by the Federal Highway Administration in Highway Statistics. On the Weiss-Stats site, we provide last year's distance driven, in thousands of miles, by each of 500 randomly selected cars. Use the technology of
In each of Exercises 9.143-9.148, we have provided a null hypothesis and alternative hypothesis and a sample from the population under consideration. In each case, use the Wilcoxon signed-rank test to perform the required hypothesis test at the 10% significance level.a. H0: Î¼ = 5, Ha: Î¼ > 5b.
Alligators perform a spinning maneuver, referred to as a "death roll", to subdue their prey. Videos were taken of juvenile alligators performing this maneuver in a study for the article "Death Roll of the Alligator, Mechanics of Twist and Feeding in Water" (Journal of Experimental Biology, Vol.
In the paper "Measurement of Ethical Food Choice Motives" (Appetite, Vol. 34, pp. 55-59), research psychologists M. Lindeman and M. VaÌˆaÌˆnaÌˆnen of the University of Helsinki published a study on the factors that most influence peoples' choice of food. One of
A manufacturer of liquid soap produces a bottle with an advertised content of 310 milliliters (mL). Sixteen bottles are randomly selected and found to have the following contents, in mL.A normal probability plot of the data indicates that you can assume the contents are normally distributed. Let
Thirty years ago, the Bureau of Justice Statistics reported in Profile of Jail Inmates that the median educational attainment of jail inmates was 10.2 years. Ten current inmates are randomly selected and found to have the following educational attainments, in years.Assume that educational
The Head Injury Criterion (HIC) is a measure of the likelihood of an injury arising from an accident such as a vehicle crash. At an HIC of 1000, one in six people will suffer a life-threatening injury to the brain. The Insurance Institute for Highway Safety performs safety rating tests on vehicles.
The convict surgeonfish is a common tropical reef fish that has been found to delay metamorphosis into adult by extending its larval phase. This delay often leads to enhanced survivorship in the species by increasing the chances of finding suitable habitat. In the paper "Delayed Metamorphosis of a
The Old Course at St. Andrews in Scotland is home of the British Open, one of the major tournaments in professional golf. The Hole O'Cross Out, known by both European and American professional golfers as one of the friendliest holes at St. Andrews, is the fifth hole, a 514-yard, par 5 hole with an
Formulate a hypothesis-testing procedure for a Wilcoxon signed-rank test that uses the test statistic z given in the preceding box. Note: Using a continuity correction provides even more accurate results?
Refer to Exercise 9.154.a. Use the procedure you formulated in Exercise 9.166 to perform the hypothesis test in Exercise 9.154.b. Compare your result in part (a) to the one you obtained in Exercise 9.154, where the normal approximation was not used?Refer to Exercise 9.154.According to the article
In this exercise, you are to obtain the distribution of the variable W for samples of size 3 so that you can see how the Wilcoxon signed-rank table is constructed.(a). The rows of the following table give all possible signs for the signed ranks in a Wilcoxon signed-rank test with n = 3. For
Assuming that the null hypothesis H0: η = η0 is true, answer the following questions. a. Why is the probability of an observation exceeding η0 equal to 0.5? b. In a simple random sample of size n, why does the number of observations that exceed η0 have a binomial distribution with parameters n
The sign test can be used whether or not the variable under consideration has a symmetric distribution. If the distribution is in fact symmetric, the Wilcoxon signed-rank test is preferable. Why do you think that is so?
What advantage does the sign test have over the Wilcoxon signed-rank test?
Define each term. a. Type I error b. Type II error c. Significance level
What does the power of a hypothesis test tell you? How is it related to the probability of making a Type II error?
What happens to the power of a hypothesis test if the sample size is increased without changing the significance level? Explain your answer.
What happens to the power of a hypothesis test if the significance level is decreased without changing the sample size? Explain your answer.
Suppose that you must choose between two procedures for performing a hypothesis test-say, Procedure A and Procedure B. Further suppose that, for the same sample size and significance level, Procedure A has less power than Procedure B. Which procedure would you choose? Explain your answer.
In each of Exercises 9.188-9.190, we have specified the "tailedness" of a hypothesis test for a population mean with null hypothesis H0: μ = μ0. For each exercise,(a). draw the ideal power curve.(b). Explain what your curve in part (a) portrays.(i) Right-tailed(ii) Left-tailed(iii) Two - tailed
In Exercises 9.191-9.196, we have given a hypothesis testing situation and(i) The population standard deviation, σ,(ii) A significance level,(iii) A sample size, and(iv) Some values of μa. For each exercise,a. Determine the probability of a Type I error.b. Apply Procedure 9.4 on page 425 to
Repeat parts (a)-(c) of Exercise 9.191 for a sample size of 20. Compare your power curves for the two sample sizes, and explain the principle being illustrated. The null and alternative hypotheses obtained in Exercise 9.15 on page 375 are, respectively, H0: μ = 0.5 ppm Ha: μ > 0.5 ppm, Where μ
Repeat parts (a)-(c) of Exercise 9.192 for a sample size of 30. Compare your power curves for the two sample sizes, and explain the principle being illustrated. Refer to Exercise 9.192: The null and alternative hypotheses obtained in Exercise 9.16 on page 375 are, respectively, H0: μ ( 23 days Ha:
Repeat parts (a)-(c) of Exercise 9.195 for a sample size of 40. Compare your power curves for the two sample sizes, and explain the principle being illustrated. Refer to 9.195, The null and alternative hypotheses obtained in Exercise 9.19 on page 375 are, respectively, H0: μ = 16.7 months Ha: μ =
Regarding the term null hypothesis: a. Originally, what did the word null in null hypothesis stand for? b. What has the term null hypothesis come to mean now?
Repeat parts (a)-(c) of Exercise 9.194 for a sample size of 15. Compare your power curves for the two sample sizes, and explain the principle being illustrated. The null and alternative hypotheses obtained in Exercise 9.18 on page 375 are, respectively, H0: μ = 55 years old Ha: μ < 55 years
Refer to the gas mileage hypothesis test of Example 9.23 on page 422. Recall that the null and alternative hypotheses are H0: μ = 26 mpg (manufacturer's claim) Ha: μ < 26 mpg (consumer group's conjecture), Where μ is the mean gas mileage of all Orions. Also recall that the mileages are normally
State two reasons why including the P-value is prudent when you are reporting the results of a hypothesis test.
Answer true or false and explain your answer: If it is important not to reject a true null hypothesis, the hypothesis test should be performed at a small significance level?
Problems 13-20 pertain to the P-value approach to hypothesis testing. a. Define the P-value of a hypothesis test. b. True or false: A P-value of 0.02 provides more evidence against the null hypothesis than a P-value of 0.03. Explain your answer. c. State the decision criterion for a hypothesis
Identify two advantages of nonparametric methods over parametric methods. When is a parametric procedure preferred? Explain your answer.
Regarding the power of a hypothesis test: a. What does it represent? b. What happens to the power of a hypothesis test if the significance level is kept at 0.01 while the sample size is increased from 50 to 100?
The Federal Bureau of Investigation (FBI) compiles information on robbery and property crimes by type and selected characteristic and publishes its findings in Uniform Crime Reports. According to that document, the mean value lost to purse snatching was $468 in 2012. For last year, 12 randomly
Refer to Problem 29.a. Perform the required hypothesis test, using the Wilcoxon signedrank test.b. In performing the hypothesis test in part (a), what assumption did you make about the distribution of last year's values lost to purse snatching?c. In Problem 29, we used the t-test to perform the
Refer to Problems 29 and 30. If in fact last year's values lost to purse snatching are normally distributed, which is the preferred procedure for performing the hypothesis test-the t-test or the Wilcoxon signed-rank test? Explain your answer.Refer to Problem 29 and 30,Refer to Problem 29.a. Perform
Refer to Problem 26. Suppose that you decide to use a z-test with a significance level of 0.10 and a sample size of 35. Assume that σ = 6.9 lb. a. Determine the probability of a Type I error. b. If last year's mean cheese consumption was 36.5 lb, identify the distribution of the variable x̅, that
Problems 34 and 35 each include a normal probability plot and either a frequency histogram or a stem-and-leaf diagram for a set of sample data. The intent is to use the sample data to perform a hypothesis test for the mean of the population from which the data were obtained. In each case, consult
Refer to Problems 34 and 35.a. In each case, consult the appropriate graphs to decide whether using the Wilcoxon signed-rank test is reasonable for performing a hypothesis test for the mean of the population from which the data were obtained. Give reasons for your answers.b. For each case where
According to the document Market Survey of Long-Term Care Costs, published by the MetLife Mature Market Institute, the average cost of a private room in a nursing home was $239 per day in 2011. A random sample of 11 nursing homes yielded the following daily costs, in dollars, for a private room in
According to Food Consumption, Prices, and Expenditures, published by the U.S. Department of Agriculture, the mean consumption of beef per person in 2011 was 57.5 lb. A sample of 40 people taken this year yielded the data, in pounds, on last year's beef consumption given on the Weiss-Stats site.
Body mass index (BMI) is a measure of body fat based on height and weight. According to 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 healthy weight
In Exercise 10.81, you conducted a non-pooled t-test to decide whether the mean number of acute postoperative days spent in the hospital is smaller with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks. a. Using a pooled t-test, repeat
Why do two normal distributions that have equal standard deviations have the same shape?
Exercises 10.113-10.116 pertain to critical values for a Mann- Whitney test. Use Table VI in Appendix A to determine the critical value(s) in each case. For a left-tailed or two-tailed test, you will also need the relation M1−A = n1 (n1 + n2 + 1) − MA. 1. n1 = 8, n2 = 9; Significance level =
The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served,
A mutual fund is a professionally managed investment that can be sold to the general public. The following table lists the 3-month rates of return, in percent, for samples of healthcare elated and technology-related mutual funds, as reported by Morningstar, an independent investment research
Refer to Exercise 10.127.a. Use the technology of your choice to obtain normal probability plots and box-plots for the two samples.b. Is it reasonable to use the pooled t-test to perform the hypothesis test required in Exercise 10.127? Explain your answer.c. Is it reasonable to use the Mann-Whitney
In the paper "The Relation of Sex and Sense of Direction to Spatial Orientation in an Unfamiliar Environment" (Journal of Environmental Psychology, Vol. 20, pp. 17-28), J. Sholl et al. published the results of examining the sense of direction of 30 male and 30 female students. After being taken to
One use of the chemical formaldehyde is to preserve animal specimens. In the article "Exposure to Formaldehyde Among Animal Health Students" (American Industrial Hygiene Association Journal, Vol. 63, pp. 647-650), A. Dufresne et al. examined student exposure to formaldehyde. In the course of their
The National Education Association collects data on teacher salaries and publishes results in Estimates of School Statistics Database. Independent samples of 100 secondary school teachers and 125 elementary school teachers yielded the data, in thousands of dollars, on annual salaries as presented
Formulate a hypothesis-testing procedure for a Mann-Whitney test that uses the test statistic z given in the preceding box?
Refer to Exercise 10.129.a. Use your procedure from Exercise 10.135 to perform the hypothesis test.b. Compare your result in part (a) to the one you obtained in Exercise 10.129 (a), where you didn't use the normal approximation.Refer to Exercise 10.129,The Federal Bureau of Prisons publishes data
In this exercise, you are to obtain the distribution of the variable M when the sample sizes are both 3. Doing so enables you to see how the Mann-Whitney table is constructed. All possible ranks for the data are displayed in the following table; the letter A stands for a member from Population 1,
Often data do not satisfy the conditions for use of any of the standard hypothesis-testing procedures that we have discussed-the pooled t-test, non-pooled t-test, or Mann- Whitney test. However, by making a suitable transformation, you can often obtain data that do satisfy the assumptions of one or
State one possible advantage of using paired samples instead of independent samples?
Provide an example (different from the ones considered in this section) of a procedure based on a paired sample being more appropriate than one based on independent samples?
Suppose that you want to perform a hypothesis test based on a simple random paired sample to compare the means of two populations and you know that the paired-difference variable has a symmetric distribution that is far from normal. a. Is use of the paired t-test acceptable if the sample size is
A hypothesis test based on a simple random paired sample is to be performed to compare the means of two populations. The sample of 15 paired differences contains an outlier but otherwise is approximately bell shaped. Assuming that removing the outlier is not legitimate, which test is better to
The American Association of University Professors (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. Pairs were formed by matching faculty in private and public institutions by rank and specialty. A random
In the Statistics Norway on-line article "The Times They Are a Changing," J. Kristiansen discussed the changes in age at the time of marriage in Norway. The ages, in years, at the time of marriage for 75 Norwegian couples is presented on the WeissStats site. Use the technology of your choice to do
In the document "Peak Discharge from Unlogged and Logged Watersheds," J. Jones and G. Grant compiled (paired) data on peak discharge from storms in two watersheds, one unlogged and one logged (100% clear-cut). If there is an effect due to clear-cutting, one would expect that the runoff would be
Assuming that the null hypothesis H0: ηd = 0 is true, answer the following questions. a. Why is the probability that an observed paired difference exceeds 0 equal to 0.5? b. In a simple random sample of size n, why does the number of paired differences that exceed 0 have a binomial distribution
The paired sign test can be used whether or not the paired difference variable has a symmetric distribution. a. If the distribution is in fact symmetric, the paired Wilcoxon signed-rank test is preferable. Why do you think that is so? b. What advantage does the paired sign test have over the paired
In each of Exercises 10.5-10.10, we have stated the purpose for performing a hypothesis test to compare the means, μ1 and μ2, of two populations. For each exercise, a. Determine the null and alternative hypotheses. Note: Always place the mean of Population 1 on the left. b. Classify the
A mutual fund is a professionally managed investment that can be sold to the general public. Mutual funds can be specialized into different categories such as healthcare-related or technology-related mutual funds. The following table lists the 3-month rates of return, in percent, for samples of
The National Association of Realtors publishes information on the cost of existing single-family homes in Median Sales Price of Existing Single-Family Homes for Metropolitan Areas. Independent random samples of 10 homes each in Atlantic City and Las Vegas yielded the following data on home prices
In the online article "Comparing the Effects of Fluoxetine and Imipramine on Total Cholesterol, Triglyceride, and Weight in Patients with Major Depression" (Journal of Pharmaceutical Sciences, Vol. 21, No. 4), E. Ananloo et al. study the effect of antidepressants on lipid profiles. Nineteen females
Suppose that independent simple random samples are taken from two populations to compare their means. Further suppose that the two distributions of the variable under consideration have the same shape. a. Would the non-pooled t-test ever be the procedure of choice in these circumstances? Explain
Suppose that a simple random paired sample is taken from two populations to compare their means. Further suppose that the distribution of the paired-difference variable has a symmetric distribution. Under what conditions would the paired t-test be preferable to the paired Wilcoxon signed-rank test?
Consider a χ2-curve with df = 16. Obtain the χ2-value that has area a. 0.025 to its left. b. 0.975 to its left. Find the required χ2-values. Illustrate your work graphically.
Determine the two χ2-values that divide the area under the curve into a middle 0.95 area and two outside 0.025 areas for a χ2-curve with a. df = 5. b. df = 26. Find the required χ2-values. Illustrate your work graphically.
Determine the two χ2-values that divide the area under the curve into a middle 0.90 area and two outside 0.05 areas for a χ2-curve with a. df = 11. b. df = 28. Find the required χ2-values. Illustrate your work graphically.
Give two situations in which making an inference about a population standard deviation would be important.
The average lactation (nursing) period of all earless seals is 23 days. Grey seals are one of several types of earless seals. The length of time that a female grey seal nurses her pup is studied by S. Twiss et al. in the article "Variation in Female Grey Seal (Halichoerus grypus) Reproductive
Gas mileage estimates for cars and light-duty trucks are determined and published by the U.S. Environmental Protection Agency (EPA). According to the EPA, ". . . the mileages obtained by most drivers will be within plus or minus 15 percent of the [EPA] estimates. . . ." Themileage estimate given
R. Morris and E.Watson studied various aspects of process capability in the paper "Determining Process Capability in a Chemical Batch Process" (Quality Engineering, Vol. 10(2), pp. 389-396). In one part of the study, the researchers compared the variability in product (as measured by standard
Homestyle Pizza of Camp Verde, Arizona, provides baking instructions for its premade pizzas. According to the instructions, the average baking time is 12 to 18 minutes. If the times are normally distributed, the standard deviation of the times should be approximately 1 minute. A random sample of 15
A coffee machine is supposed to dispense 6 fluid ounces (fl oz) of coffee into a paper cup. In reality, the amounts dispensed vary from cup to cup. However, if the machine is working properly, most of the cups will contain within 10% of the advertised 6 fl oz. In other words, the standard deviation
In Issue 10 of STATS from Iowa State University, data were published from an experiment that examined the effects of machine adjustment on bolt production. An electronic counter records the number of bolts passing it on a conveyer belt and stops the run when the count reaches a preset number. The
Refer to Exercise 11.21 and find a 90% confidence interval for the standard deviation of lactation periods of grey seals.
Refer to Exercise 11.22 and find a 95% confidence interval for the standard deviation of highway gas mileages for all cars of the model in question.
Refer to Exercise 11.23 and determine a 98% confidence interval for the product variability of the piece of equipment under consideration.
Refer to Exercise 11.24 and determine a 98% confidence interval for the standard deviation of baking times.
Refer to Exercise 11.25 and obtain a 90% confidence interval for the standard deviation of the amounts of coffee being dispensed.
Refer to Exercise 11.26 and obtain a 90% confidence interval for the standard deviation of the times needed to count 20 bolts.
The annual update of U.S. Overseas Loans and Grants, informally known as the "Greenbook," contains data on U.S. government monetary economic and military assistance loans. The following table shows military assistance loans, in thousands of dollars, to a sample of 10 countries, as reported by the
The amount of solar energy transmitted through each square meter of space prior to entry in the earth's atmosphere, as measured by satellites, is called the total solar irradiance (TSI). A random sample of daily TSI measurements, in watts per square meter, from the World Radiation Center in
One extinct relative of primates that lived in North America about 60 million years ago is called Plesiadapis cookei. Dental characteristics of P. cookei were compared to those of other primate species in the article "Evidence of Dietary Differentiation among Late Paleocene-Early Eocene
In Example 11.4 on page 516, we stated that, based on standards set by the United States Pharmacopeia (USP), a standard deviation of Xenical capsule weights of less than 2 mg is acceptable. We now ask you to obtain that result. In doing so, we presume that weights of Xenical capsules are normally
Measured on the Stanford Revision of the Binet-Simon Intelligence Scale, intelligence quotients (IQs) are known to be normally distributed with a mean of 100 and a standard deviation of 16. Use the technology of your choice to do the following.a. Simulate 1000 samples of four IQs each.b. Determine
Consider an F-curve with df = (6, 8). Determine the F-value that has area a. 0.01 to its left. b. 0.95 to its left. Use Table VIII and, if necessary, the reciprocal property of F-curves to find the required F-values. Illustrate your work graphically.
Consider an F-curve with df = (15, 5). Determine the F-value that has area a. 0.025 to its left. b. 0.975 to its left. Use Table VIII and, if necessary, the reciprocal property of F-curves to find the required F-values. Illustrate your work graphically.

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