Question

the dean of the engineering school at a technical university wants to emphasize the importance of having students who are gifted at reading and writing as well as math. she wants to know if she can accurately claim that graduate students in engineering programs at her school have significantly higher scores on the verbal reasoning section of the gre (a standardized test used in the admissions process for many graduate programs) than the national average for engineering students. the national average for the verbal reasoning gre score for engineering students was 150 with a standard deviation of 9. a random sample of 49 engineering graduate students at her school were found to have an average verbal reasoning gre score of 153. after analyzing the data to determine whether the mean verbal reasoning gre score of the engineering graduate students at the technical university is higher than the national average, the p - value of 0.0099 was obtained. using a 0.05 significance level, what conclusion can be drawn from the data? a. do not reject the null hypothesis. the average verbal reasoning gre score of the engineering graduate students at the technical university is not higher than the population average. b. do not reject the null hypothesis. the average verbal reasoning gre score of the engineering graduate students at the technical university is higher than the population average. c. reject the null hypothesis. the average verbal reasoning gre score of the engineering graduate students at the technical university is not higher than the population average. d. reject the null hypothesis. the average verbal reasoning gre score of the engineering graduate students at the technical university is higher than the population average.

Explanation:

Step1: Recall p - value decision rule

If p - value < significance level, reject the null hypothesis.

Step2: Compare p - value and significance level

The p - value is 0.0099 and the significance level is 0.05. Since 0.0099 < 0.05.

Step3: Determine conclusion

We reject the null hypothesis. The null hypothesis is usually that the mean of the sample is not higher than the population mean. Rejecting it means the average verbal reasoning GRE score of the engineering graduate students at the technical university is higher than the population average.

Answer:

D. Reject the null hypothesis. The average verbal reasoning GRE score of the engineering graduate students at the technical university is higher than the population average.