atment group, 119 were free from headaches 15 minutes after treatment. Among the 151 patients given the placebo, 38 were free from headaches 15 minutes after treatment. Use a 0.05 significance level to test the im that the oxygen treatment is effective. Complete parts (a) through (c) below. O E. Ho: P1 = P2 D. Ho: P1 = P2 H1: P1 *P2 OF. Ho: P1 S 2 H4: P1 #P2 H1: P1

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In a study of treatments for very painful "cluster" headaches, 145 patients were treated with oxygen and 151 other patients were given a placebo consisting of ordinary air. Among the 145 patients in the oxygen treatment group, 119 were free from headaches 15 minutes after treatment. Among the 151 patients given the placebo, 38 were free from headaches 15 minutes after treatment. Use a 0.05 significance level to test the claim that the oxygen treatment is effective. Complete parts (a) through (c) below.

- **O D.**  
  \( H_0: p_1 = p_2 \)  
  \( H_1: p_1 \neq p_2 \)  

- **O E.**  
  \( H_0: p_1 = p_2 \)  
  \( H_1: p_1 < p_2 \)  

- **O F.**  
  \( H_0: p_1 \leq p_2 \)  
  \( H_1: p_1 \neq p_2 \)  

**Identify the test statistic.**

z = [ ]

(Round to two decimal places as needed.)

**Identify the P-value.**

P-value = [ ]

(Round to three decimal places as needed.)

**What is the conclusion based on the hypothesis test?**

The P-value is [ ] the significance level of \(\alpha = 0.05\), so [ ] the null hypothesis. There [ ] evidence to support the claim that the cure rate with oxygen treatment is higher than the cure rate for those given a placebo.

**b. Test the claim by constructing an appropriate confidence interval.**

The 90% confidence interval is [ ] < \( (p_1 - p_2) \) < [ ]

(Round to three decimal places as needed.)

**What is the conclusion based on the confidence interval?**

Because the confidence interval limits [ ] 0, it appears that the two cure rates are [ ] Because the confidence interval limits include [ ] values, it appears that the cure rate is [ ].
Transcribed Image Text:In a study of treatments for very painful "cluster" headaches, 145 patients were treated with oxygen and 151 other patients were given a placebo consisting of ordinary air. Among the 145 patients in the oxygen treatment group, 119 were free from headaches 15 minutes after treatment. Among the 151 patients given the placebo, 38 were free from headaches 15 minutes after treatment. Use a 0.05 significance level to test the claim that the oxygen treatment is effective. Complete parts (a) through (c) below. - **O D.** \( H_0: p_1 = p_2 \) \( H_1: p_1 \neq p_2 \) - **O E.** \( H_0: p_1 = p_2 \) \( H_1: p_1 < p_2 \) - **O F.** \( H_0: p_1 \leq p_2 \) \( H_1: p_1 \neq p_2 \) **Identify the test statistic.** z = [ ] (Round to two decimal places as needed.) **Identify the P-value.** P-value = [ ] (Round to three decimal places as needed.) **What is the conclusion based on the hypothesis test?** The P-value is [ ] the significance level of \(\alpha = 0.05\), so [ ] the null hypothesis. There [ ] evidence to support the claim that the cure rate with oxygen treatment is higher than the cure rate for those given a placebo. **b. Test the claim by constructing an appropriate confidence interval.** The 90% confidence interval is [ ] < \( (p_1 - p_2) \) < [ ] (Round to three decimal places as needed.) **What is the conclusion based on the confidence interval?** Because the confidence interval limits [ ] 0, it appears that the two cure rates are [ ] Because the confidence interval limits include [ ] values, it appears that the cure rate is [ ].
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