Q: If $$n = 900$$, $$p_0 = 0.62$, and $$\hat{p} = 0.58$$, what is the standard error used in the z$-test for proportions?

$$\sqrt{\frac{0.62 \times 0.38}{900}}$$

Question 1

Which of the following is the correct symbolic representation of the null hypothesis when testing the claim that the proportion of computers with antivirus software is 93%?

Accepted Answer

$$H_0$$: p = 0.93$$

Question 2

A researcher wants to test if the proportion of married Americans has decreased from 62%. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: p \u003c 0.62$$

Question 3

Which of the following requirements must be checked before performing a hypothesis test for a population proportion?

Accepted Answer

The sample is randomly selected, there are two categories, and $$np \geq 5$$ and $$nq \geq 5$$

Question 4

Given a sample of 400 computers, 380 have antivirus software. Test the claim that $$p = 0.93 at$$ $$\alpha = 0.05. $$What is the value of the test statistic $$z$$?

Accepted Answer

$$z = 1.04$$

Question 5

In Example 1, the P-value is greater than $$\alpha. $$What is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not sufficient evidence to reject the claim.

Question 6

A sample of 900 adults finds 522 are married. Test the claim that the proportion is now less than 62% at $$\alpha = 0.01. $$What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{522}{900} = 0.58$$

Question 7

Which formula is used to calculate the test statistic $$z$$ for a population proportion?

Accepted Answer

$$z = \frac{\hat{p} - p_0$}{\sqrt{\frac{p_0$ q_0$}{n}}}$$

Question 8

If the P-value is less than the significance level $$\alpha$$, what is the correct decision in hypothesis testing?

Accepted Answer

Reject the null hypothesis

Question 9

A company claims that at least 80% of its products pass quality control. A random sample of 200 products finds 150 pass. At $$\alpha = 0.05$$, what is the null hypothesis?

Accepted Answer

$$H_0$$: p = 0.80$$

Question 10

Which of the following scenarios is appropriate for using a hypothesis test for a population proportion?

Accepted Answer

Testing if the proportion of defective items in a shipment exceeds 5%

Question 11

A medical researcher claims that 70% of patients recover after a new treatment. In a sample of 120 patients, 78 recover. What is the value of $$q_0$$ used in the test statistic formula?

Accepted Answer

$$q_0 = 1 - 0.70 = 0.30$

Question 12

Which step comes immediately after converting the sample statistic into the test statistic in the hypothesis testing process?

Accepted Answer

Use either a critical value or P-value to test the null hypothesis

Question 13

A school administrator wants to know if less than 60% of students use the library weekly. In a sample of 250 students, 130 report using the library weekly. What is the alternative hypothesis?

Accepted Answer

$$H_1$$: p \u003c 0.60$$

Question 14

If $$n = 900$$, $$p_0 = 0.62$, and $$\hat{p} = 0.58$$, what is the standard error used in the z$-test for proportions?

Accepted Answer

$$\sqrt{\frac{0.62 	imes 0.38}{900}}$$

Question 15

A city claims that 75% of its residents recycle. A survey of 160 residents finds 110 recycle. At $$\alpha = 0.05$$, what is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{110}{160} = 0.6875$$

Question 16

Which of the following best describes the meaning of 'fail to reject the null hypothesis' in the context of hypothesis testing?

Accepted Answer

There is not enough evidence to support the alternative hypothesis

Question 17

A random sample of 500 voters finds 320 support a new law. The city claims 70% support. What is the value of $$p_0$$ for the hypothesis test?

Accepted Answer

$$p_0 = 0.70$

Question 18

Which of the following is NOT a requirement for using the normal approximation in hypothesis testing for proportions?

Accepted Answer

The population standard deviation is known

Question 19

A hypothesis test for a proportion yields a P-value of 0.03. If $$\alpha = 0.01$$, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis

Hypothesis Testing for a Population Proportion

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