a. χ205 with df = 5b. χ 2025 with df = 15c. χ 2975 with df = 20d. χ 2oi with df = 10e. χ 295 with df = 18
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11.2 A sample of 20 items provides a sample standard deviation of 5.
a. Compute the 90% confidence interval estimate of the population variance.
b. Compute the 95% confidence interval estimate of the population variance.
c. Compute the 95% confidence interval estimate of the population standard deviation.
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11.3 A sample of 16 items provides a sample standard deviation of 9.5. Test the following hypotheses using a = .05. What is your conclusion? Use both the p-value approach and the critical value approach....
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11.4 The variance in drug weights is critical in the pharmaceutical industry. For a specific drug, with weights measured in grams, a sample of 18 units provided a sample variance of s2 = .36.
a. Construct a 90% confidence interval estimate of the population variance for the weight of this drug.
b. Construct a 90% confidence interval estimate of the population standard deviation.
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11.5 The daily car rental rates for a sample of eight cities follow....
a. Compute the variance and the standard deviation for these data.
b. What is the 95% confidence interval estimate of the variance of car rental rates for the population?
c. What is the 95% confidence interval estimate of the standard deviation for the population?
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11.6 The Fidelity Growth Income mutual fund received a three-star, or neutral, rating from Morningstar. Shown here are the quarterly percentage returns for the five-year period from 2001 to 2005 (Morningstar Funds 500, 2006)....
a. Compute the mean, variance, and standard deviation for the quarterly returns.
b. Financial analysts often use standard deviation as a measure of risk for stocks and mutual funds. Develop a 95% confidence interval for the population standard deviation of quarterly returns for the Fidelity Growth Income mutual fund.
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11.7 To analyze the risk, or volatility, associated with investing in Chevron Corporation common stock, a sample of the monthly total percentage return for 12 months was taken. The returns for the 12 months of 2005 are shown here (Compustat, February 24, 2006). Total return is price appreciation plus any dividend paid....
a. Compute the sample variance and sample standard deviation as a measure of volatility of monthly total return for Chevron.
b. Construct a 95% confidence interval for the population variance.
c. Construct a 95% confidence interval for the population standard deviation.
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11.8
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11.9 An automotive part must be machined to close tolerances to be acceptable to customers. Production specifications call for a maximum variance in the lengths of the parts of .0004. Suppose the sample variance for 30 parts turns out to be s2 = .0005. Using a = .05, test to see whether the population variance specification is being violated.
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11.10 The average standard deviation for the annual return of large cap stock mutual funds is 18.2% (The Top Mutual Funds, AAII, 2004). The sample standard deviation based on a sample of size 36 for the Vanguard PRIMECAP mutual fund is 22.2%. Construct a hypothesis test that can be used to determine whether the standard deviation for the Vanguard fund is greater than the average standard deviation for large cap mutual funds. With a .05 level of significance, what is your conclusion?
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11.11
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11.12 A Fortune study found that the variance in the number of vehicles owned or leased by subscribers to Fortune magazine is .94. Assume a sample of 12 subscribers to another magazine provided the following data on the number of vehicles owned or leased: 2, 1, 2, 0, 3, 2, 2, 1, 2, 1, 0, and 1.
a. Compute the sample variance in the number of vehicles owned or leased by the 12 subscribers.
b. Test the hypothesis H0: σ2 = .94 to determine whether the variance in the number of vehicles owned or leased by subscribers of the other magazine differs from σ2 = .94 for Fortune .At a a.05 level of significance what is your conclusion?
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11.13 Find the following F distribution values from Table 4 of Appendix B.
a. F05 with degrees of freedom 5 and 10b. F025 with degrees of freedom 20 and 15c. F01 with degrees of freedom 8 and 12d. F10 with degrees of freedom 10 and 20
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11.14 A sample of 16 items from population 1 has a sample variance ... and a sample of 21 items from population 2 has a sample variance .... Test the following hypotheses at the .05 level of significance....
a. What is your conclusion using the p-value approach?
b. Repeat the test using the critical value approach.
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11.15 Consider the following hypothesis test....
a. What is your conclusion if n1 = 21, s 1 = 8.2, n2 = 26, and s2 = 4.0? Use a = .05 and the p-value approach.
b. Repeat the test using the critical value approach.
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11.16
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11.17 Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170 and a sample of 25 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100.
a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.
b. At a .01 level of significance, what is your conclusion? What is the p-value? Discuss the reasonableness of your findings.
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11.18
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11.19 The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?...
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11.20 On the basis of data provided by a Romaic salary survey, the variance in annual salaries for seniors in public accounting firms is approximately 2.1 and the variance in annual salaries for managers in public accounting firms is approximately 11.1. The salary data were provided in thousands of dollars. Assuming that the salary data were based on samples of 25 seniors and 26 managers, test the hypothesis that the population variances in the salaries are equal. At a .05 level of significance, what is your conclusion?
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11.21 Fidelity Magellan is a large cap growth mutual fund and Fidelity Small Cap Stock is a small cap growth mutual fund (Morningstar Funds 500, 2006). The standard deviation for both funds was computed based on a sample of size 26. For Fidelity Magellan, the sample standard deviation is 8.89%; for Fidelity Small Cap Stock, the sample standard deviation is 13.03%. Financial analysts often use the standard deviation as a measure of risk. Conduct a hypothesis test to determine whether the small cap growth fund is riskier than the large cap growth fund. Use a = .05 as the level of significance.
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11.22 A research hypothesis is that the variance of stopping distances of automobiles on wet pavement is substantially greater than the variance of stopping distances of automobiles on dry pavement. In the research study, 16 automobiles traveling at the same speeds are tested for stopping distances on wet pavement and then tested for stopping distances on dry pavement. On wet pavement, the standard deviation of stopping distances is 32 feet.On dry pavement, the standard deviation is 16 feet.
a. At a .05 level of significance, do the sample data justify the conclusion that the variance in stopping distances on wet pavement is greater than the variance in stopping distances on dry pavement? What is the p-value?
b. What are the implications of your statistical conclusions in terms of driving safety recommendations?
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11.23 Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms.
a. What is the point estimate of the population variance?
b. Provide a 90% confidence interval estimate of the population variance.
c. Provide a 90% confidence interval estimate of the population standard deviation.
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11.24 Initial public offerings (IPOs) of stocks are on average underpriced. The standard deviation measures the dispersion, or variation, in the underpricing-overpricing indicator. A sample of 13 Canadian IPOs that were subsequently traded on the Toronto Stock Exchange had a standard deviation of 14.95. Develop a 95% confidence interval estimate of the population standard deviation for the underpricing-overpricing indicator.
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11.25 The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs....
a. Compute the sample mean.
b. Compute the sample standard deviation.
c. Compute a 95% confidence interval for the population standard deviation.
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11.26 Part variability is critical in the manufacturing of ball bearings. Large variances in the size of the ball bearings cause bearing failure and rapid wearout. Production standards call for a maximum variance of .0001 when the bearing diameters are measured in inches. A sample of 15 bearings shows a sample standard deviation of .014 inches.
a. Use a = .10 to determine whether the sample indicates that the maximum acceptable variance is being exceeded.
b. Compute the 90% confidence interval estimate of the variance of the ball bearings in the population.
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11.27 The filling weight for boxes of cereal is designed to have a variance .02 ounces or less. A sample of 41 boxes of cereal shows a sample standard deviation of .16 ounces. Use a = .05 to determine whether the variance in the cereal box filling weight is exceeding the design specification.
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11.28 City Trucking, Inc., claims consistent delivery times for its routine customer deliveries. A sample of 22 truck deliveries shows a sample variance of 1.5 minutes. Test to determine whether H0: o2 can be rejected. Use a = .10.
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11.29 A sample of 9 days over the past 6 months showed that a dentist treated the following numbers of patients: 22, 25, 20, 18, 15, 22, 24, 19, and 26. If the number of patients seen per day is normally distributed, would an analysis of these sample data reject the hypothesis that the variance in the number of patients seen per day is equal to 10? Use a .10 level of significance. What is your conclusion?
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11.30 A sample standard deviation for the number of passengers taking a particular airline flight is 8. A 95% confidence interval estimate of the population standard deviation is 5.86 passengers to 12.62 passengers.
a. Was a sample size of 10 or 15 used in the statistical analysis?
b. Suppose the sample standard deviation of s = 8 was based on a sample of 25 flights. What change would you expect in the confidence interval for the population standard deviation? Compute a 95% confidence interval estimate of o with a sample size of 25.
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11.31
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11.32 The grade point averages of 352 students who completed a college course in financial accounting have a standard deviation of .940. The grade point averages of 73 students who dropped out of the same course have a standard deviation of .797. Do the data indicate a difference between the variances of grade point averages for students who completed a financial accounting course and students who dropped out? Use a .05 level of significance. Note: F025 with 351 and 72 degrees of freedom is 1.466.
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11.33 The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use a = .10.
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11.34 Two new assembly methods are tested and the variances in assembly times are reported. Use a = .10 and test for equality of the two population variances....
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