Student attitudes. The Survey of Study Habits and Attitudes (SSHA)

is a psychological test that measures students’ study habits and attitude 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 σ = 30. The teacher wants to test the hypotheses H0: μ = 115 Ha: μ > 115

(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 μ and σ on a Normal curve.)

(b) Suppose that the sample data give x = 118.6. Mark this point on the axis of your sketch. In fact, the outcome was x = 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 P-value for the sample result x = 125.7.

502 CHAPTER 22 What Is a Test of Significance?