## Answers

**Solution:-**

**7) (c)**

**State the hypotheses.** The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P_{1} = P_{2}

Alternative hypothesis: P_{1} < P_{2}

Note that these hypotheses constitute a one-tailed test.

**Formulate an analysis plan**. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

**Analyze sample data**. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p_{1} * n_{1} + p_{2} * n_{2}) / (n_{1} + n_{2})

p = 0.48

SE = sqrt{ p * ( 1 - p ) * [ (1/n_{1}) + (1/n_{2}) ] }

SE = 0.09992

z = (p_{1} - p_{2}) / SE

z = - 2.40

where p_{1} is the sample proportion in sample 1, where p_{2} is the sample proportion in sample 2, n_{1} is the size of sample 1, and n_{2} is the size of sample 2.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than -2.40.

Thus, the P-value = 0.0082

**Interpret results**.

Since the P-value (0.0082) is less than the significance level (0.05), we have to reject the null hypothesis.

**From the above test we have sufficient evidence in the favor of the claim that new drug is effective.**

**8) (b) 95% confidence interval for the difference between the two proportions is C.I = ( - 0.43, - 0.05).**

C.I = (0.36 - 0.60) + 1.96 × 0.0969

C.I = - 0.24 + 0.190

**C.I = ( - 0.43, - 0.05)**