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Why do small firms export? Refer to the Journal of Small
Chapter 7, Problem 95E(choose chapter or problem)
Problem 95E
Why do small firms export? Refer to the Journal of Small Business Management (Vol. 40, 2002) study of what motivates small firms to export, Exercise 7.45 (p. 379). Recall that 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 = 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 (as in Exercise 7.45) if the standard deviation of the scale scores is too large.
b. Give the largest value of the true standard deviation, , for which you will reject the null hypothesis H0: = 3.5 in favor of the alternative hypothesis Ha: > 3.5 using = .01.
c. Based on the study results, is there evidence (at = .01) to indicate that is smaller than the value you determined in part b?
Questions & Answers
QUESTION:
Problem 95E
Why do small firms export? Refer to the Journal of Small Business Management (Vol. 40, 2002) study of what motivates small firms to export, Exercise 7.45 (p. 379). Recall that 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 = 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 (as in Exercise 7.45) if the standard deviation of the scale scores is too large.
b. Give the largest value of the true standard deviation, , for which you will reject the null hypothesis H0: = 3.5 in favor of the alternative hypothesis Ha: > 3.5 using = .01.
c. Based on the study results, is there evidence (at = .01) to indicate that is smaller than the value you determined in part b?
ANSWER:
Solution
Step 1 of 3
a) Here the sample mean is 3.85
Since the sample mean is not that far from the value 3.5
A large standard deviation indicate that the value 3.85 is not very many standard deviations from 3.5