# 3 Hypothesis test questions

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Question 1 - the concepts

Professor Walters knows that the mean score on the midterm exam from all the years he has been teaching is 83%. Kennedy was in his most recent class, and his class's mean score on the final exam was 81%. Kennedy decided to run a hypothesis test to determine if the mean score of his class was different than the mean score of the population. α = .01.

• What is the mean score of the population?

• What is the mean score of the sample?

• Is this test one-tailed or two-tailed? Why?

• What are the null and alternative hypotheses in this case?

• Let's pretend that p was calculated, and p = 0.005, should Kennedy reject or fail to reject the null hypothesis? Why?

• What should Kennedy's statement of conclusion be? (This circles back to what is being tested).

Question 2 - hypothesis test with guidance

A sample of 14 account balances of a credit company showed a mean customer balance of $4,550, but the marketing manager claimed that the mean balance for the population was $4,325. The marketing manager did NOT have the population standard deviation, but the sample standard deviation was found to be $500. Use the p-value approach to conduct a full hypothesis test (all steps) that can be used to determine whether the mean of all account balances is significantly different from $4,325. Let α = .10.

To help you go through the steps of hypothesis testing, follow these prompts:

The null hypothesis is

The alternative hypothesis is

I will use a _________ in my formula because

I have calculated the value of t to be

I have used t to get the value of p. My p value is

Alpha, which is given in the problem, is

When I compared p to alpha, p is __________ alpha.

Because of this, I know I should __________ my null hypothesis.

Choose one. The mean balance is different than $4325. / The mean balance is NOT different than $4325.

Question 3 -on your own

A sample of 510 homes for sale in ABC City showed a mean asking price of $258,000, but the city claimed that the mean asking price for the population was $249,000. The population standard deviation of all homes for sale was $9,000. Use the p-value approach to conduct a full hypothesis test (all steps- follow the guidance in the last problem) that can be used to determine whether the mean asking price is significantly greater than $249,000. Let α = .05.

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Question 1 - the concepts

• What is the mean score of the population? 83%

• What is the mean score of the sample? 81%

• Is this test one-tailed or two-tailed? Why? This would be a two-tailed test because we are trying to determine if the mean score of his class was different than the mean score of the population.

• What are the null and alternative hypotheses in this case?

Hₒ: µ = 83% and Hₐ: µ ≠ 83%

• Let's pretend that p was calculated, and p = 0.005, should Kennedy reject or fail to reject the null hypothesis? Why? With a p-value of 0.005 Kennedy should reject the null ...

###### Education

- MSc, California State Polytechnic University, Pomona
- MBA, University of California, Riverside
- BSc, California State Polytechnic University, Pomona
- BSc, California State Polytechnic University, Pomona

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