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 correct hypotheses are:
H₀: $\mu$ = 20,H₁: $\mu$ > 20

Question

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 correct hypotheses are:
H₀:

\mu

= 20,H₁:

\mu

> 20

Quizplus · Accepted Answer

The correct hypothesis should be:
H0: μ = 20
H1: μ < 20
since the portfolio manager thinks the average P/E ratio is too high, hence he is testing for a decrease in the average P/E ratio. The null hypothesis assumes that the population mean is equal to 20, while the alternative hypothesis assumes that the population mean is less than 20.

A Portfolio Manager Was Analyzing the Price-Earnings Ratio for This μ\muμ

A Portfolio Manager Was Analyzing the Price-Earnings Ratio for This $\mu$