22.31} Student attitudes. The Survey of Study Habits and Attitudes [SSHAJ is a psychological test that measures students' study habits and attitudes toward school. Scores range from t] to 200. The mean score for US. college students is about 1151 and the standard deviation is about 30. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to 25 students who are at least 31] years old. Assume that scores in the population of older students are Normally distributed with standard deviation 9' = 31}. The teacher wants to test the hypotheses HE]: pt = 11 5 Ha: Ju :- 11 5 {a} What is the sampling distribution of the mean score 3: of a sample of 25 older students if the null hypothesis is true? Sketch the density curve of this distribution. (Hint: Sketch a Normal curve first, then mark the axis using what you know about locating p. and a on a Normal curve.) (b) Suppose that the sample data give 3?: 113.6. Mark this point on the axis of your sketch In fact, the outcome was T: 125.7. Mark this point on your sketch. Using your sketch, explain in simple language why one outcome is good evidence that the mean score of all older students is greater than 115 and why the other outcome is not. (c) Shade the area under the curve that is the Pvalue for the sample result T= 125.7