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# Statistics: Two-Tailed Tests and Test Statistic

101

Find the sample proportions and test statistic for equal proportions. Is the decision close? Find the p-value.
a. Dissatisfied workers in two companies: x1 = 40, n1 = 100, x2 = 30, n2 = 100, α = .05, two tailed test.
b. Rooms rented at least a week in advance at two hotels: x1 = 24, n1 = 200, x2 = 12, n2 = 50, α = .01, left-tailed test.
c. Home equity loan default rates in two banks: x1 = 36, n1 = 480, x2 = 26, n2 = 520, α = .05, right-tailed test.

104
From her firm's computer telephone log, an executive found that the mean length of 64 telephone calls during July was 4.48 minutes with a standard deviation of 5.87 minutes. She vowed to make an effort to reduce the length of calls. The August phone log showed 48 telephone calls whose mean was 2.396 minutes with a standard deviation of 2.018 minutes. (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value assuming unequal variances. Interpret these results using α = .01. (c) Why might the sample data not follow a normal, bell-shaped curve? If not, how might this affect your conclusions?

#### Solution Summary

This solution shows step-by-step calculations to determine the null and alternative hypothesis for each case as well as calculates the test statistic and compares it to the p-value. A decision is then made to accept or reject the null hypothesis.

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