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: $\mu \geq$ 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 \geq

20,H₁:

\mu

< 20.

Quizplus · Accepted Answer

The correct hypotheses for testing if the actual mean P/E ratio is less than the stated average of 20 would be $H_0: \mu \geq 20$ (null hypothesis) and $H_1: \mu < 20$ (alternative hypothesis), which matches the provided notation.

A Portfolio Manager Was Analyzing the Price-Earnings Ratio for This μ≥\mu \geqμ≥

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