Q: Which of the following best describes the null hypothesis ($$H_0) in a $$hypothesis test about a population proportion?

$$H_0$$: p = \text{some value}$$

Question 1

Which of the following best describes the null hypothesis ($$H_0) in a $$hypothesis test about a population proportion?

Accepted Answer

$$H_0$$: p = 	ext{some value}$$

Question 2

A researcher claims a new teaching method increases student performance. The school’s average score has been 75. Which is the correct set of hypotheses for a one-sided test?

Accepted Answer

$$H_0$$: \mu = 75,\ H_a: \mu \u003e 75$$

Question 3

What does a P-value represent in the context of hypothesis testing?

Accepted Answer

The probability of observing a sample statistic as extreme as the one observed, assuming the null hypothesis is true.

Question 4

Suppose you conduct a one-proportion z-test and obtain a P-value of 0.03 with $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is strong evidence for $$H_a.$$

Question 5

Which of the following is NOT a condition to check before performing a one-sample t-test for the mean?

Accepted Answer

There are at least 10 successes and 10 failures in the sample.

Question 6

A factory claims their new process reduces the proportion of defective items below 5%. Which is the correct alternative hypothesis?

Accepted Answer

$$H_a: p \u003c 0.05$$

Question 7

If the P-value is greater than the significance level $$\alpha$$, what is the correct decision?

Accepted Answer

Fail to reject $$H_0$$

Question 8

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting $$H_0$$ when $$H_0 is $$actually true.

Question 9

Which formula gives the test statistic for a one-sample z-test for a proportion?

Accepted Answer

$$z = \frac{\hat{p} - p_0$}{\sqrt{\frac{p_0$(1-p_0$)}{n}}}$$

Question 10

A university wants to test if a new program increases retention rates above 92%. Which is the correct null and alternative hypothesis?

Accepted Answer

$$H_0$$: p = 0.92,\ H_a: p \u003e 0.92$$

Question 11

Which of the following is the correct formula for the test statistic in a one-sample t-test for the mean?

Accepted Answer

$$t = \frac{\bar{x} - \mu_0$}{\frac{s}{\sqrt{n}}}$$

Question 12

Which of the following best describes a two-tailed hypothesis test for a mean?

Accepted Answer

$$H_a: \mu 
eq \mu_0$

Question 13

Suppose you roll a die 10 times and get 4 sixes. Which test would you use to determine if the die is fair?

Accepted Answer

One-proportion z-test

Question 14

Which of the following is NOT a correct interpretation of 'Fail to Reject $$H_0$$'?

Accepted Answer

We have insufficient evidence to conclude anything.

Question 15

Which of the following is the correct P-value calculation for a two-tailed z-test?

Accepted Answer

$$2P(Z \geq |z|)$$

Question 16

Which of the following is a common significance level ($$\alpha) $$used in hypothesis testing?

Accepted Answer

$$0.05$$

Question 17

Suppose you want to estimate the proportion of defective items produced by a manufacturing process. Can you use the methods of this chapter?

Accepted Answer

Yes

Question 18

Which of the following is the correct P-value calculation for a right-tailed z-test?

Accepted Answer

$$P(Z \geq z)$$

Question 19

Which of the following is the correct P-value calculation for a left-tailed z-test?

Accepted Answer

$$P(Z \leq z)$$

Chapter 15: Testing Hypotheses – Study Notes

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