5. Student attitudes. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitudes toward school. Scores range from 0 to 200. The mean score for U.S. college students is about 115, 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 30 years old. Assume that scores in the population of older students are Normally distributed with standard deviation = 30. The teacher wants to test the hypotheses

(a) What is the sampling distribution of the mean score x 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 and on a Normal curve.)

(b) Suppose that the sample mean is = 125.7. Mark this point on the axis of your sketch. Shade the area under the curve that is the P-value for the sample result = 125.7.

(c)What is the test statistic?What is the P-value?

(d)Do we reject the null hypothesis or do we fail to reject the null hypothesis?Why?

(e)Write the conclusion of the hypothesis test in the context of the problem.Use complete sentences.