The Journal of Small Business Management (Vol. 40, 2002) published a study of what motivates small firms to export. In a survey of 137 exporting firms, each CEO was asked to respond to the statement "Management believes that the firm can achieve economies of scale by exporting" on a scale of 1 (strongly disagree) to 5 (strongly agree). Summary statistics for the n = 137 scale scores were reported as x̅ = 3.85 and s = 1.5.

a. Explain why the researcher will be unable to conclude that the true mean scale score exceeds 3.5 if the standard deviation of the scale scores is too large.

b. Give the largest value of the true standard deviation, s, for which you will reject the null hypothesis H0: μ = 3.5 in favor of the alternative hypothesis Ha: μ > 3.5 using α = .01.

c. Based on the study results, is there evidence (at a = .01) to indicate that s is smaller than the value you determined in part b?

d. The scale scores for the sample of 137 small firms are unlikely to be normally distributed. Does this invalidate the inference made about μ in part b? About s in part c?