Hypothesis Testing: Remission Time & Depressed Individuals

14) Medical researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic mental illness established two independent test groups. The first group consisted of 9 people with the illness, and the second group consisted of 12 people with the illness. The first group received treatment 1 and had a mean time until remission of 165 days, with a standard deviation of 8 days. The second group received treatment 2 and had a mean time until remission of days, with a standard deviation of 5 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the 0.05 level of significance, that the mean number of days before remission after treatment 1 (mean 1), is less than the mean number of days before remission after treatment 2 (mean 2)?
Perform a one-tailed test...Carry your intermediate computations to at least three decimal places and round your answers.
? The null hypothesis
? The alternate hypothesis
? The type of test statistic
? The value of the test statistic(round three decimal places)
? The critical value at the 0.05 level of significance.
Can we conclude that the mean number of days before remission after treatment 1 in less than the mean number of days before remission after treatment 2? (yes or no)

15) Two popular drugs used for the treatment of depression are Resithan and Exemor. A random sample of 501 depressed individuals is selected and treated with Resithan, and 215 find relief from their depression. A random sample of 594 depressed individuals is independently selected from the first sample and treated with Exemor, and 261 find relief from their depression. Can we conclude, at the 0.05 level of significance, that the proportion (P1)of depressed individuals taking Resithan who find relief from depression is less than the proportion (P2) of all depressed individuals taking Exemor who find relief from depression?
Perform a one-tailed test...Carry your intermediate computations to at least three decimal places and round your answers.
? The null hypothesis
? The alternate hypothesis
? The type of test statistic
? The value of the test statistic(round three decimal places)
? The critical value at the 0.05 level of significance.
Can we conclude that the proportion of depressed individuals taking Resithan who find relief is less than the proportion taking Exemor who find relief? (yes or no)