Question20. A company claims that it has a mean customer service score of 78 (out of 100). You examine 150 customer reviews and find that the mean score of those reviews is 73 with a standard deviation of 2 . Test the accuracy of the company's claim at the $2 \%$ significance level.
Proposed Solution: $H_{0}: \mu=78$ $H_{a}: \mu<78$ (since $\bar{x}$ is less than 78 ) Rejection Region: qt(0.02,149); $\mathbf{<}-2.07$ Test Statistic: $\mathrm{t}=(73-78) /(2 /$ sqrt $(150))=-30.61$ In rejection region: (RHo) P-Value Test: pt(-30.61,149) $=0 \%$ $p<\alpha(R H o)$ The customer value score is lower than the claimed 78. What is wrong with the proposed solution? A. A z-test should have been used instead of t-test. B. $\hat{p}$ should be calculated as $78 / 100=0.78$ and a proportion test used. C. The alternate hypothesis is not supported by the question. D. For $p<\alpha$, the wrong conclusion was drawn. E. There is nothing wrong with the proposed solution.