Concept explainers
a Based on your answers to Exercises 13.20 and 13.21 and the comments at the end of this section, how would you expect confidence intervals computed using the results of this section to compare with related intervals that make use of the data from only one or two of the samples obtained in a one-way layout? Why?
b Refer to part (a). Is it possible that a 95% confidence interval for the mean of a single population based only on the sample taken from that population will be shorter than the 95% confidence interval for the same population mean that would be obtained using the procedure of this section? How?
13.20 Refer to Examples 13.2 and 13.3.
a Use the portion of the data in Table 13.2 that deals only with teaching technique 1 and the method of Section 8.8 to form a 95% confidence interval for the mean score of students taught using technique 1.
b How does the length of the 95% confidence interval that you found in part (a) compare to the length of the 95% confidence interval obtained in Example 13.3?
c What is the major reason that the interval that you found in part (a) is longer than the interval given in Example 13.3?
13.21 Refer to Examples 13.2 and 13.4.
a Use the portion of the data in Table 13.2 that deals only with teaching techniques 1 and 4 and the method of Section 8.8 to form a 95% confidence interval for the difference in mean score for students taught using techniques 1 and 4.
b How does the length of the 95% confidence interval that you found in part (a) compare to the length of the 95% confidence interval obtained in Example 13.4?
c What is the major reason that the interval that you found in part (a) is longer than the interval given in Example 13.4?
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