Question

In a survey of 173 publicly-traded companies, the average price-earnings ratio was 18.3 with a standard deviation of 7.9. When testing the hypothesis (at the 5% level of significance) that the average energy use has decreased from the past value of 16.6, what is the test statistic? (please round your answer to 2 decimal places)

Answer 1

Hypothesis

$\\\mu_c = \text{current average price earning ratio}\\ \mu_p = \text{past average price earning ratio}\\\\ H_0 : \mu_c<\mu_p\\ H_1 : \mu_c>\mu_p\\\\$

$\mu_c= 18.3\\ \mu_p=16.6\\ \sigma = 7.9\\ tstat = \frac{18.3-16.6}{\frac{7.9}{\sqrt{173}}}=2.83 \\$

Using t-table we find
Pvalue = 0.002601563

Since the pvalue is less than 0.05, we reject the null hypothesis and conclude that the current average price earnings ratio has not decreased from the past value.