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Questions and Answers of
Statistics
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
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
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
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,
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
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
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
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
In the paper "Measurement of Ethical Food Choice Motives" (Appetite, Vol. 34, pp. 55-59), research psychologists M. Lindeman and M. VaÌaÌnaÌnen of the
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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%
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
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
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
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
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
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.
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
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.
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.
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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