# Null and Alternative Hypothesis

The educational testing service (ETS) designs and administers the SAT exams. Recently the format of the exam changed and the claim has been made that the new exam can be completed in an average time of 120 minutes. A sample of 50 new exam times yielded an average time of 115 min. The standard deviation is assumed to be 2 minutes.

a. Set up the null and the alternative hypotheses to test if average time to complete the exam has changed from 120 minutes.

b. Test your hypothesis using alpha = 0.05

c. Find p value

d. Based on the p value, what can you conclude about the average time to complete the new exam?

https://brainmass.com/statistics/hypothesis-testing/null-and-alternative-hypothesis-8074

#### Solution Preview

Solution. Let us denote the time to complete the new exam by X. Assume that X follows normal distribution N(a,b^2), where a is the mean of X and b is the standard deviation.

<br> Define the hypothesis as follows.

<br>

<br>Null hypothesis H0 and the Alternative hypothesis H1.

<br>

<br>a) H0:a=120;

<br> H1: a is not equal to 120.

<br>

<br>b) ...

#### Solution Summary

The educational testing service (ETS) designs and administers the SAT exams. Recently the format of the exam changed and the claim has been made that the new exam can be completed in an average time of 120 minutes. A sample of 50 new exam times yielded an average time of 115 min. The standard deviation is assumed to be 2 minutes.

a. Set up the null and the alternative hypotheses to test if average time to complete the exam has changed from 120 minutes.

b. Test your hypothesis using alpha = 0.05

c. Find p value

d. Based on the p value, what can you conclude about the average time to complete the new exam?