MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion \( p \) at the given level of significance \( \alpha \) using the given sample statistics.

**Claim:** \( p \neq 0.22 \); \( \alpha = 0.10 \); Sample statistics: \( \hat{p} = 0.18 \), \( n = 150 \).

---

**Can the normal sampling distribution be used?**

- A. Yes, because \( pq \) is greater than \( \alpha = 0.10 \.
- B. Yes, because both \( np \) and \( nq \) are greater than or equal to 5.
- C. No, because \( np \) is less than 5.
- D. No, because \( nq \) is less than 5.

**State the null and alternative hypotheses.**

- A. \( H_0: p \le 0.22 \)  
  \( H_a: p > 0.22 \)
  
- B. \( H_0: p \ge 0.22 \)  
  \( H_a: p < 0.22 \)

- C. \( H_0: p = 0.22 \)  
  \( H_a: p \neq 0.22 \)

- D. The test cannot be performed.

**Determine the critical value(s).** Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- A. The critical value(s) is/are \(\_\_\)
  (Round to two decimal places as needed. Use a comma to separate answers as needed.)
  
- B. The test cannot be performed.

**Find the z-test statistic.** Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- A. \( z = \_\_\)
  (Round to two decimal places as needed.)
  
- B. The test cannot be performed.

**What is the result of the test?**

- A. Fail to reject \( H_0 \). The data provide sufficient evidence to support the claim.
  
- B. Reject \( H_0 \). The data do not provide sufficient evidence to support the claim.

- C. Reject \( H_0 \). The data provide sufficient evidence to support the claim.
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Transcribed Image Text:Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion \( p \) at the given level of significance \( \alpha \) using the given sample statistics. **Claim:** \( p \neq 0.22 \); \( \alpha = 0.10 \); Sample statistics: \( \hat{p} = 0.18 \), \( n = 150 \). --- **Can the normal sampling distribution be used?** - A. Yes, because \( pq \) is greater than \( \alpha = 0.10 \. - B. Yes, because both \( np \) and \( nq \) are greater than or equal to 5. - C. No, because \( np \) is less than 5. - D. No, because \( nq \) is less than 5. **State the null and alternative hypotheses.** - A. \( H_0: p \le 0.22 \) \( H_a: p > 0.22 \) - B. \( H_0: p \ge 0.22 \) \( H_a: p < 0.22 \) - C. \( H_0: p = 0.22 \) \( H_a: p \neq 0.22 \) - D. The test cannot be performed. **Determine the critical value(s).** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. The critical value(s) is/are \(\_\_\) (Round to two decimal places as needed. Use a comma to separate answers as needed.) - B. The test cannot be performed. **Find the z-test statistic.** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. \( z = \_\_\) (Round to two decimal places as needed.) - B. The test cannot be performed. **What is the result of the test?** - A. Fail to reject \( H_0 \). The data provide sufficient evidence to support the claim. - B. Reject \( H_0 \). The data do not provide sufficient evidence to support the claim. - C. Reject \( H_0 \). The data provide sufficient evidence to support the claim.
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