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 =0.10, can it be concluded that there is a difference in the lengths of the essays between the two groups? Science majors 1545 3051 2554 3521 2703 1947 2918 3993 3352 1731 3854 3539 Humanities majors 2713 2060 2448 2786 1958 2284 1668 2907 2566 2803 Send data to Excel Use 1 for the mean of science majors and 2 for the mean of humanities majors. Assume the populations are normally distributed, and that the variances are unequal. Part 1 of 5 (a) State the hypotheses and identify the claim with the correct hypothesis. H0 : =12 not claim H1 : 12 claim This hypothesis test is a two-tailed test. Part 2 of 5 (b) Find the critical value. Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas. Critical value(s): , 2.093 Correct