Music performance anxiety. Refer to the British Journal of Music Education (Mar. 2014) study of performance anxiety by music students, Exercise 2.39 (p. 78). 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 in eight different studies.

54 42 51 39 41 43 55 40 Source: Patston, T. “Teaching stage fright?—Implications for music educators.” British Journal of Music Education, Vol. 31, No. 1, Mar. 2014

(adapted from Figure 1).

a. Compute the mean PAI value, x, for the sample of 8 LO6 studies. (See your answer to Exercise 2.62a.)

b. Compute the standard deviation of the PAI values, s, for the sample of 8 studies. (See your answer to Exercise 2.87b.)

c. Use the results, parts a and

b, to form a 95% confidence interval for μ, the true mean PAI value for the population of all similar music performance anxiety studies.

d. For the interval, part

c, to be valid, how should the population of PAI values for all music performance anxiety studies be distributed?

e. If you were to repeatedly sample eight music performance anxiety studies and form a 95% confidence interval for μ for each sample, what proportion of the intervals will actually contain the true value of μ?