Question

QUESTION 16

1. A person is conducting a hypothesis test. Suppose their p-value turns out to be .0001. What does this mean?

	A.	They have strong evidence to reject the null hypothesis.
	B.	They do not have enough evidence to reject the null hypothesis.

QUESTION 17

1. Aaron would like to test his guess about the percent of RCSJ students who say they play video games on a daily basis. He guesses this value to be 72%. Based on a random sample of 190 RCSJ students, 146 of them say they play video games daily. Was his guess reasonable? Assume 95% confidence.

(Hint: You can use either a confidence interval or a hypothesis test to answer this question!)

	A.	Yes, his guess was reasonable.
	B.	No, his guess was not reasonable.

QUESTION 18

1. Kim would like to estimate the average cost of an apartment per month in a certain city. She guesses that a 2-bedroom apartment will be $875 per month. Based on a random sampling of forty 2-bedroom apartment listings, she finds a sample mean of $925 per month with a standard deviation of $110 per month. Was her guess reasonable? Assume 95% confidence. (Hint: You may use either a confidence interval or hypothesis test to help you answer this question.)

	A.	Yes, her guess was reasonable.
	B.	No, her guess was not reasonable.

Answer 1

Question 16. Answer is

A. They have strong evidence to reject the null hypothesis.

Question 17 Answer is

A. Yes, his guess was reasonable

Question 18 Answer is

B. No, her guess was not reasonable.

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Explanations and calculations

Question 16. Answer is

A. They have strong evidence to reject the null hypothesis.

For smaller p-values, , we reject the null hypothesis. In our case p- value is 0.0001, which is a very small quantity. By definition of p-value , we can say that the p- value is the evidence against a null hypothesis. This means, the smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

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Question 17 Answer is

A. Yes, his guess was reasonable

The test statistic for z-test for proportion is given by

and confidence interval for proportion is given by

In the given problem, for

Hence 95% confidence interval becomes

Since 0.72 belongs to this interval we conclude that his guess was reasonable

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Question 18 Answer is

B. No, her guess was not reasonable.

The test statistic for testing mean is given by

and the confidence interval for mean is given by

In the given problem

Hence confidence interval becomes

Since 875 lies outside this interval we conclude that her guess was not reasonable.