The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample 49 42 mean Sample 84 90 variance Sample size 10 18 The degrees of freedom for the $t$ distribution are a. 20 b. 19 c. 17 d. 18
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Step 1: Calculate the pooled sample variance using the formula: \[ s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2} \] where \( n_1 \) and \( n_2 \) are the sample sizes, and \( s_1^2 \) and \( s_2^2 \) are the sample variances. Show more…
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Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample mean 45 42 Sample variance 85 90 Sample size 10 12 Refer to Exhibit 10-4. The degrees of freedom for the t distribution are ____. 22 21 20 19
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