# Null and Alternative Hypothesis

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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?

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##### 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?

##### 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) ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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