Q: A coin is spun 400 times and lands heads 54.5% of the time. Test the claim that the coin is biased towards heads. What is the value of the test statistic?

$$z = \frac{0.545 - 0.50}{\sqrt{\frac{0.50 \times 0.50}{400}}} = 1.8$$

Q: A survey of 1011 people finds that 495 support stricter gun control laws. Test the claim that the proportion has changed from 0.52. What are the correct null and alternative hypotheses?

$$H_0$$: p = 0.52$$, H_a$$: p \neq 0.52$$

Question 1

Which of the following best describes the null hypothesis in a hypothesis test for a population proportion?

Accepted Answer

It is a claim that the population proportion is equal to a specific value.

Question 2

A researcher wants to test if the proportion of left-handed pitchers in Major League Baseball is greater than the general population proportion of 10%. What is the correct form of the alternative hypothesis?

Accepted Answer

$$H_a: p \u003e 0.10$$

Question 3

Which of the following is a requirement for using the normal model in a one-proportion z-test?

Accepted Answer

The sample must have at least 10 expected successes and 10 expected failures.

Question 4

Given $$n = 400$$ and $$p = 0.20$$, what is the standard error for the sampling distribution of the sample proportion?

Accepted Answer

$$\sqrt{\frac{(0.20)(0.80)}{400}} = 0.02$$

Question 5

A coin is spun 400 times and lands heads 54.5% of the time. Test the claim that the coin is biased towards heads. What is the value of the test statistic?

Accepted Answer

$$z = \frac{0.545 - 0.50}{\sqrt{\frac{0.50 	imes 0.50}{400}}} = 1.8$$

Question 6

What does a p-value represent in the context of hypothesis testing for population proportions?

Accepted Answer

The probability of observing a test statistic as extreme as or more extreme than the one obtained, assuming the null hypothesis is true.

Question 7

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

Accepted Answer

Reject the null hypothesis.

Question 8

A survey of 1011 people finds that 495 support stricter gun control laws. Test the claim that the proportion has changed from 0.52. What are the correct null and alternative hypotheses?

Accepted Answer

$$H_0$$: p = 0.52$$, H_a$$: p 
eq 0.52$$

Question 9

Which of the following best describes the significance level $$\alpha in $$hypothesis testing?

Accepted Answer

The probability of rejecting the null hypothesis when it is true.

Question 10

A researcher claims that 17% of young people ages 2-19 are obese. She believes the value should be higher. In a random sample of 200, 42 are obese. What is the sample proportion?

Accepted Answer

$$\hat{p} = \frac{42}{200} = 0.21$$

Question 11

Which of the following is NOT a condition required for performing a one-proportion z-test?

Accepted Answer

Sample mean greater than population mean

Question 12

In a hypothesis test, what does it mean if the p-value is greater than the significance level $$\alpha$$?

Accepted Answer

Fail to reject the null hypothesis.

Question 13

A county supervisor believes her county has a different proportion of Hispanic people than the national proportion of 16%. What is the correct alternative hypothesis?

Accepted Answer

$$H_a: p 
eq 0.16$$

Question 14

Which of the following statements about statistical significance and practical significance is TRUE?

Accepted Answer

Practical significance means the result is both statistically significant and meaningful.

Question 15

A musicologist claims she can distinguish between Mozart and Haydn with a success rate greater than 50%. She gets 9 out of 10 correct. If the p-value is 0.011 and the significance level is 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis and conclude she has some ability.

Question 16

Which formula is used to calculate the test statistic for a one-proportion z-test?

Accepted Answer

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

Question 17

In a two-sided hypothesis test, which alternative hypothesis is correct?

Accepted Answer

$$H_a: p 
eq p_0$

Question 18

A voting study finds that 40 out of 54 political scientists voted, while the general population proportion is 0.47. What is the sample proportion?

Accepted Answer

$$\hat{p} = \frac{40}{54} \approx 0.74$$

Chapter 8: Hypothesis Testing for Population Proportions

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