A portfolio manager was analyzing the price-earnings ratio for this year's performance.His boss said that the average price-earnings ratio was 20 for the many stocks,which his firm had traded,but he felt that figure was too high.The portfolio manager randomly selected a sample of 50 P/E ratios and found a mean of 18.17 and standard deviation of 4.60.Assume that the population is normally distributed and test at the 0.01 level of significance.
The decision rule is: Reject H₀ if the calculated t < -2.405.

Question

Quizplus · Accepted Answer

The decision rule for a one-tailed t-test at the 0.01 level of significance with a sample size of 50 (which gives 49 degrees of freedom) involves comparing the calculated t-value to a critical t-value. The critical t-value for a one-tailed test with 49 degrees of freedom at the 0.01 level of significance is approximately -2.405. Therefore, if the calculated t-value is less than -2.405, the null hypothesis (that the true mean is equal to 20) would be rejected in favor of the alternative hypothesis that the true mean is less than 20.

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