QUESTION 10 In a survey of 120 publicly-traded companies, the average price-earnings ratio was 18.5 with a standard deviation of 8.2 . When testing the hypothesis (at the [a]\% level of significance) that the average energy use has decreased from the past value of 16.8 , the p-value is 0.0116 . Therefore, if you are using a \( 10 \% \) level of significance that the average price-earnings ratio has decreased from the past, what is your conclusion concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesis

To determine whether to reject or fail to reject the null hypothesis, we need to compare the p-value to the significance level. 1. **Identify the significance level**: The problem states that we are using a \( 10\% \) level of significance, which can be expressed as \( \alpha = 0.10 \). 2. **Identify the p-value**: The p-value given in the problem is \( 0.0116 \). 3. **Compare the p-value to the significance level**: - If the p-value is less than the significance level (\( p < \alpha \)), we reject the null hypothesis. - If the p-value is greater than or equal to the significance level (\( p \geq \alpha \)), we fail to reject the null hypothesis. In this case: - \( p = 0.0116 \) - \( \alpha = 0.10 \) Since \( 0.0116 < 0.10 \), we reject the null hypothesis. ### Conclusion: We reject the null hypothesis, which suggests that there is sufficient evidence to conclude that the average price-earnings ratio has decreased from the past value.