Music performance anxiety. Refer to the British Journal of Music Education (Mar. 2014) study of performance anxiety by music students, Exercise 7.37 (p. 362). Recall that the Performance Anxiety Inventory (PAI) was used to measure music performance anxiety on a scale from 20 to 80 points. The table below gives PAI values for participants LO9 in eight different studies. A MINITAB printout of the data analysis is shown.

54 42 51 39 41 43 55 40

a. Set up the null and alternative hypotheses for determining whether the mean PAI value, m, for all similar studies of music performance anxiety exceeds 40.

b. Find the rejection region for the test, part

a, using a = .05.

c. Compute the test statistic.

d. State the appropriate conclusion for the test.

e. What conditions are required for the test results to be valid?

f. Locate the p-value for the test on the MINITAB printout and use it to make a conclusion. (Your conclusion should agree with your answer in part d.)
g. How would your conclusion change if you used a = .01?

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One-Sample T: PAI Test of mu = 40 vs > 40 Variable N Mean StDev SE Mean PAI 8 45.63 6.59 2.33 95% Lower Bound T P 41.21 2.41 0.023