Question

Question 2 – Social Responsibility of Business The Nobel prize winning “monetarist” economist Milton Friedman made a famous but very controversial assertion that “the social responsibility of business is to increase its profits”. Corporate social responsibility has become a hot topic of discussion, and an independent research group has claimed that at least 54% of Canadians agree with the Friedman assertion. You take a random sample of 125 people and find only 57 agreeing with the Friedman assertion.

a) Test whether the random sample constitutes sufficient evidence to disprove the research group's claim. Use the p-value approach and a 5% level of significance.

b) Calculate the appropriate one-sided 95% confidence interval. How would you use this interval to complete the test above?

c) Suppose you want to estimate the proportion of Canadians who agree with the Friedman assertion, using a margin of error of ± 2% for a 95% two-sided confidence interval. What sample size would be required?

Answer 1

a) Test whether the random sample constitutes sufficient evidence to disprove the research group's claim. Use the p-value approach and a 5% level of significance.

H0: p 0.54

Ha: p < 0.54

p̂ = 57/125 = 0.456

The test statistic, z = (p̂ - p)/√p(1-p)/n = (0.456 - 0.54)/√0.54(1-0.54)/125 = -1.88

The p-value is 0.0298.

Since the p-value (0.0298) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we have sufficient evidence to disprove the research group's claim.

b) Calculate the appropriate one-sided 95% confidence interval. How would you use this interval to complete the test above?

The 95% confidence interval is:

= p ± z*(√p(1-p)/n

= 0.456 ± 1.96*(√0.456(1-0.456)/125

= (0.369, 0.543)

c) Suppose you want to estimate the proportion of Canadians who agree with the Friedman assertion, using a margin of error of ± 2% for a 95% two-sided confidence interval. What sample size would be required?

Sample size = (1.96/0.02)2*(0.456)*(1-0.456) = 2383

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