depression. Can we conclude, at the 0.05 level of significance, that the proportion pj of all depressed individuals taking Resithan who find relief from depression is greater than the proportion pɔ of all depressed individuals taking Exemor who find relief from depression?

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**Title: Hypothesis Testing for Depression Treatment Efficacy**

Two popular drugs used for the treatment of depression are Resithan and Exemor. A random sample of 534 depressed individuals is selected and treated with Resithan, and 184 find relief from their depression. A random sample of 431 depressed individuals is independently selected from the first sample and treated with Exemor, and 137 find relief from their depression. 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 and round your answers as specified in the parts below. (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.**

\( \text{(Choose one) } \, \Box \)

**(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.)**

[ ]

**(e) Can we conclude that the proportion of depressed individuals taking Resithan who find relief is greater than the proportion taking Exemor who find relief?**

\( \bigcirc \) Yes 

\( \bigcirc \) No 

**Notes:**

- The image includes a table for hypothesis testing, with a selection menu for choosing the type of test statistic.
- The icons to the right depict statistical symbols and operations.

This structured approach helps easily identify the hypotheses, choose the appropriate statistical test, compute necessary values, and reach a conclusion based on the evidence presented.
Transcribed Image Text:**Title: Hypothesis Testing for Depression Treatment Efficacy** Two popular drugs used for the treatment of depression are Resithan and Exemor. A random sample of 534 depressed individuals is selected and treated with Resithan, and 184 find relief from their depression. A random sample of 431 depressed individuals is independently selected from the first sample and treated with Exemor, and 137 find relief from their depression. 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 and round your answers as specified in the parts below. (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.** \( \text{(Choose one) } \, \Box \) **(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.)** [ ] **(e) Can we conclude that the proportion of depressed individuals taking Resithan who find relief is greater than the proportion taking Exemor who find relief?** \( \bigcirc \) Yes \( \bigcirc \) No **Notes:** - The image includes a table for hypothesis testing, with a selection menu for choosing the type of test statistic. - The icons to the right depict statistical symbols and operations. This structured approach helps easily identify the hypotheses, choose the appropriate statistical test, compute necessary values, and reach a conclusion based on the evidence presented.
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