Questions: from a random sample of 15 customers at each branch. Complete parts (a) through (d) below C. Do not reject H0. There is insufficient evidence that the mean waiting time between the two branches differ. D. Reject H0. There is insufficient evidence that the mean waiting time between the two branches differ b. Determine the p-value in (a) and interpret its meaning p-value =0 (Round to three decimal places as needed) Interpret the p-value Choose the correct answer below A. It is the probability the two banks have different population mean waiting times c. In addition to equal variances, what other assumption is necessary in (a)? A. The sample sizes must be equal B. The samples are specifically chosen and not independently sampled C. Both sampled populations are approximately normal D. Both sampled populations are not approximately normal

Solution Steps

The Standard Error $SE$ is calculated using the formula:

$$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{\frac{0.317}{15} + \frac{0.119}{15}} = 0.17$$

The test statistic $t$ is computed as follows:

$$t = \frac{\bar{x}_1 - \bar{x}_2}{SE} = \frac{6.033 - 6.473}{0.17} = -2.581$$

The degrees of freedom $df$ are calculated using the formula:

$$df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 - 1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 - 1}} = \frac{0.001}{0.0} = 23.234$$

The p-value $P$ is calculated as:

$$P = 2(1 - T(|t|)) = 2(1 - T(2.581)) = 0.017$$

Based on the results:

• The calculated $t$-statistic is $-2.581$.
• The p-value is $0.017$.
• The degrees of freedom are $23.234$.
• The critical value at $\alpha = 0.05$ is $2.068$.

Since $P < 0.05$, we reject the null hypothesis $H_0$. There is sufficient evidence that the mean waiting time between the two branches differs.

In addition to equal variances, the assumption that both sampled populations are approximately normal is necessary.

Final Answer