For the following data, compute the test statistic and the critical value, and determine whether to reject $H _ { 0 }$ at the $\alpha = 0.10$ level. $\begin{array} { l | l | l | l | l | l | l | l | l } \text { Sample A } & 40 & 51 & 51 & 45 & 42 & 44 & 43 & 53 \ \hline \text { Sample B } & 25 & 40 & 34 & 51 & 29 & 29 & 38 & 62 \end{array}$ A) S=5, Critical value is 6, Reject H₀ B) S=5, Critical value is 6, Do not reject H₀ C) S=6, Critical value is 4, Reject H₀ D) S=6, Critical value is 4, Do not reject H₀

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Quizplus · Accepted Answer

The sample mean of Sample A is 46 and the sample mean of Sample B is 39. The sample standard deviation of Sample A is 5.29 and the sample standard deviation of Sample B is 12.58. The test statistic is:$$t = \frac{\overline{x}_1 - \overline{x}_2}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$$$$t = \frac{46 - 39}{5.29 \sqrt{\frac{1}{8} + \frac{1}{8}}}$$$$t = 2.12$$The critical value for a two-tailed test with $\alpha = 0.10$ and 14 degrees of freedom is 1.761. Since the test statistic (2.12) is greater than the critical value (1.761), we reject the null hypothesis.

For the Following Data, Compute the Test Statistic and the Critical