Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H:0 H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0

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**Hypothesis Testing for Depression Treatments**

Based on advancements in drug therapy, a pharmaceutical company is developing Resithan, a new treatment for depression. A medical researcher for the company is studying the effectiveness of Resithan compared to their existing drug, Exemor. A random sample of 509 depressed individuals is selected and treated with Resithan, and 218 find relief from their depression. A random sample of 429 depressed individuals is independently selected from the first sample and treated with Exemor, and 172 find relief from their depression.

Based on the medical researcher’s study, can we conclude, at the 0.05 level of significance, that the proportion \( p_1 \) of all depressed individuals taking Resithan who find relief from depression is greater than the proportion \( p_2 \) of all depressed individuals taking Exemor who find relief from depression?

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).

\( H_0 : \)  
\( H_1 : \)  

(b) Determine the type of test statistic to use.

(Choose one)  

(c) Find the value of the test statistic. (Round to three or more decimal places.)

[_____]  

(d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.)

[_____]  

**Interactive Components:**

- The user can enter their hypotheses in the text fields provided.
- The type of test statistic (e.g., Z, t) can be selected from a dropdown menu.
- Fields are provided to input the calculated test statistic and critical value.
- A ‘Start’ button allows users to initiate the test process.

**Additional Tools:**

- Links to relevant tutorials or formulas for conducting the statistical test.
- Explanation of statistical significance and the importance of hypothesis testing in clinical research.

This module is designed to facilitate understanding of hypothesis testing in the context of comparative drug effectiveness studies.
Transcribed Image Text:**Hypothesis Testing for Depression Treatments** Based on advancements in drug therapy, a pharmaceutical company is developing Resithan, a new treatment for depression. A medical researcher for the company is studying the effectiveness of Resithan compared to their existing drug, Exemor. A random sample of 509 depressed individuals is selected and treated with Resithan, and 218 find relief from their depression. A random sample of 429 depressed individuals is independently selected from the first sample and treated with Exemor, and 172 find relief from their depression. Based on the medical researcher’s study, can we conclude, at the 0.05 level of significance, that the proportion \( p_1 \) of all depressed individuals taking Resithan who find relief from depression is greater than the proportion \( p_2 \) of all depressed individuals taking Exemor who find relief from depression? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \). \( H_0 : \) \( H_1 : \) (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) [_____] (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) [_____] **Interactive Components:** - The user can enter their hypotheses in the text fields provided. - The type of test statistic (e.g., Z, t) can be selected from a dropdown menu. - Fields are provided to input the calculated test statistic and critical value. - A ‘Start’ button allows users to initiate the test process. **Additional Tools:** - Links to relevant tutorials or formulas for conducting the statistical test. - Explanation of statistical significance and the importance of hypothesis testing in clinical research. This module is designed to facilitate understanding of hypothesis testing in the context of comparative drug effectiveness studies.
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