During the last decade a number of institutions dedicated to improving the quali

Question

During the last decade a number of institutions dedicated to improving the quality of products and services in the United States have been formed. Many of these groups annually give awards to companies that produce high-quality goods and services. An investor believes that publicly traded companies that win awards are likely to outperform companies that do not win such awards. The help determine his return on investment in such companies, he took a random sample of 83 firms that won quality awards the previous year and computed that annual return had he invested: x¯ = 15.02% with s = 8.31%.

(a) Report the 95% confidence interval for µ, the average annual return.

(b) The investor expected that he had an average return of 15%. Based upon your confidence interval in part (a), is there sufficient evidence at the 5% significance level that the investor’s expectation didn’t become true. Explain

Explanation / Answer

a) here std error of mean =std deviation/(n)1/2 =8.31/(86)1/2 =0.912

for (n-1=82) degree of freedom ; crtiical value of t =1.9893

therefore 95% confidence interval for µ =sample mean -/+ t*Std error =13.2055 to 16.8345

b) as above interval contains 15% as possible value for expected annual return therefore we did not have  sufficient evidence at the 5% significance level that the investor’s expectation didn’t become true

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