QuestionGUIDED SOLUTION
Essays A professor wishes to see if two groups of students' essays differ in lengths, that is, the number of words in each essay. The professor randomly selects 12 essays from a group of students who are science majors and 10 essays from a group of humanities majors to compare. The data are shown. At $\alpha=0.10$, can it be concluded that there is a difference in the lengths of the essays between the two groups?
Science majors $$\begin{array}{llllllllll} \text { Science majors } \\ \hline 2057 & 3129 & 2501 & 3464 & 2762 & 2075 & 2984 & 3783 & 3259 & 2389 \\ 3939 & 3425 \end{array}$$
Humanities majors $$\begin{array}{l} \text { Humanities majors } \\ \hline 2698 \\ \hline 2940 \\ 2257 \\ 19332 \\ 1740 \end{array}$$
Send data to Excel Use $\mu_{1}$ for the mean of science majors and $\mu_{2}$ for the mean of humanities majors. Assume the populations are normally distributed, and that the variances are unequal. (a) State the hypotheses and identify the claim with the correct hypothesis. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. (a) State the hypotheses and identify the claim with the correct hypothesis.
The null hypothesis $H_{0}$ is the statement that there is (Choose one) $\nabla$ between the means. This is equivalent to $\mu_{1}$ (Choose one) $\nabla \mu_{2}$.