Chapter 8: Q4E (page 465)
To use the t-statistic to test for a difference between the means of two populations, what assumptions must be made about the two populations? About the two samples?
The T Statistic is used in a T-test to determine whether to accept as well as deny the empty hypothesis.
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Question: Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise 6.29 (p. 348). Recall that the variable of interest was the average distance separating traps—called trap-spacing—deployed by teams of fishermen. The trap-spacing measurements (in meters) for a sample of seven teams from the Bahia Tortugas (BT) fishing cooperative are repeated in the table. In addition, trap-spacing measurements for eight teams from the Punta Abreojos (PA) fishing cooperative are listed. For this problem, we are interested in comparing the mean trap-spacing measurements of the two fishing cooperatives.
BT Cooperative | 93 | 99 | 105 | 94 | 82 | 70 | 86 | |
PA Cooperative | 118 | 94 | 106 | 72 | 90 | 66 | 98 |
Source: Based on G. G. Chester, “Explaining Catch Variation Among Baja California Lobster Fishers Through Spatial Analysis of Trap-Placement Decisions,” Bulletin of Marine Science, Vol. 86, No. 2, April 2010 (Table 1).
a. Identify the target parameter for this study.b. Compute a point estimate of the target parameter.c. What is the problem with using the normal (z) statistic to find a confidence interval for the target parameter?d. Find aconfidence interval for the target parameter.e. Use the interval, part d, to make a statement about the difference in mean trap-spacing measurements of the two fishing cooperatives.f. What conditions must be satisfied for the inference, part e, to be valid?
Salmonella in yield. Salmonella infection is the most common bacterial foodborne illness in the United States. How current is Salmonella in yield grown in the major agricultural region of Monterey, California? Experimenters from the U.S. Department of Agriculture (USDA) conducted tests for Salmonella in yield grown in the region and published their results in Applied and Environmental Microbiology (April 2011). In a sample of 252 societies attained from water used to wash the region, 18 tested positive for Salmonella. In an independent sample of 476 societies attained from the region's wildlife (e.g., catcalls), 20 tested positive for Salmonella. Is this sufficient substantiation for the USDA to state that the frequency of Salmonella in the region's water differs from the frequency of Salmonella in the region's wildlife? Use a = .01 to make your decision
A random sample of size n = 121 yielded = .88.
a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain.
b. Construct a 90% confidence interval for p.
c. What assumption is necessary to ensure the validity of this confidence interval?
To compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:
Sample 1 | Sample 2 |
a. Use a confidence interval to estimate the difference between the population means . Interpret the confidence interval.
b. Test the null hypothesis versus the alternative hypothesis . Give the significance level of the test and interpret the result.
c. Suppose the test in part b was conducted with the alternative hypothesis . How would your answer to part b change?
d. Test the null hypothesis versus . Give the significance level and interpret the result. Compare your answer with the test conducted in part b.
e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a–d?
Question: Refer to the Journal of Business Logistics (Vol. 36, 2015) study of the factors that lead to successful performance-based logistics projects, Exercise 2.45 (p. 95). Recall that the opinions of a sample of Department of Defense (DOD) employees and suppliers were solicited during interviews. Data on years of experience for the 6 commercial suppliers interviewed and the 11 government employees interviewed are listed in the accompanying table. Assume these samples were randomly and independently selected from the populations of DOD employees and commercial suppliers. Consider the following claim: “On average, commercial suppliers of the DOD have less experience than government employees.”
a. Give the null and alternative hypotheses for testing the claim.
b. An XLSTAT printout giving the test results is shown at the bottom of the page. Find and interpret the p-value of the test user.
c. What assumptions about the data are required for the inference, part b, to be valid? Check these assumptions graphically using the data in the PBL file.
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