Q: A scientist claims that the proportion of people who support a new policy is 0.5. In a sample of 200, 110 support the policy. What is the value of the test statistic $$z$$?

$$z = \frac{0.55 - 0.5}{\sqrt{0.5 \times 0.5 / 200}}$$

Question 1

Which of the following conditions must be satisfied before performing a hypothesis test about a population proportion?

Accepted Answer

The sample must be a simple random sample, and both $$np \geq 5$$ and $$nq \geq 5$$ must be satisfied.

Question 2

A researcher wants to test if more than 40% of patients respond to a new drug. In a sample of 200 patients, 90 responded. What is the null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: p = 0.40$$

Question 3

What is the formula for the test statistic $$z$$ when testing a claim about a proportion?

Accepted Answer

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

Question 4

In the OxyContin study, 127 subjects were tested and 12 developed nausea. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{12}{127}$$

Question 5

A poll finds that 481 out of 1200 adults favor stem cell funding. What is the value of $$q$$ for this sample?

Accepted Answer

$$q = 1 - \hat{p}$$, \hat{p} = \frac{481}{1200}$$, so q = 1$$ - \frac{481}{1200}$

Question 6

Which calculator function would you use to convert a z-score to a p-value when testing a proportion?

Accepted Answer

"normalcdf"

Question 7

If the calculated z-statistic is 2.09 and the critical value for a right-tailed test at $$\alpha = 0.05 is 1.64$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$ because $$z \u003e 1.64$$

Question 8

Which of the following best describes the p-value method for hypothesis testing?

Accepted Answer

Compare the p-value to $$\alpha$$; if p-value $$\u003c \alpha$$, reject $$H_0.$$

Question 9

A scientist claims that the proportion of people who support a new policy is 0.5. In a sample of 200, 110 support the policy. What is the value of the test statistic $$z$$?

Accepted Answer

$$z = \frac{0.55 - 0.5}{\sqrt{0.5 	imes 0.5 / 200}}$$

Question 10

Which step comes immediately after stating the null and alternative hypotheses when testing a claim about a proportion?

Accepted Answer

Select the significance level $$\alpha$$

Question 11

In a left-tailed test about a proportion, which of the following would be the correct alternative hypothesis?

Accepted Answer

$$H_1$$: p \u003c $$p_0$$

Question 12

Why must both $$np \geq 5$$ and $$nq \geq 5 be $$satisfied when testing a claim about a proportion?

Accepted Answer

To ensure the sampling distribution of $$\hat{p} is $$approximately normal.

Question 13

A medical researcher wants to test if less than 25% of patients experience side effects. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: p \u003c 0.25$$

Question 14

In the stem cell survey example, what is the null hypothesis if the claim is that the proportion in favor equals 0.5?

Accepted Answer

$$H_0$$: p = 0.5$$

Question 15

If a p-value is calculated as 0.037 and the significance level $$\alpha is 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$ because $$0.037 \u003c 0.05$$

Question 16

Which of the following is NOT a step in the summary of steps for testing a claim about a proportion?

Accepted Answer

Calculate the sample mean.

Question 17

A researcher uses the shortcut calculator function "1-PropZTest". What does this function compute?

Accepted Answer

It calculates the test statistic and p-value directly for a proportion.

Question 18

If the sample proportion $$\hat{p} is 0.20$$, the claimed proportion $$p is 0.25$$, and the sample size $$n is 150$$, what is the denominator in the test statistic formula?

Accepted Answer

$$\sqrt{0.25 	imes 0.75 / 150}$$

Question 19

Which of the following real-world scenarios is most appropriate for a hypothesis test about a proportion?

Accepted Answer

Testing whether more than 60% of voters support a new law.

Testing a Claim About a Proportion (Hypothesis Testing for Proportions)

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