Question

The first two pictures are different questions and the rest of the pics are the parts that go with both of them.

Answer 1

Que.1

Here n = 231. and p = 0.91

np₀ (1-p₀) = 231 * 0.91 * 0.09 = 18.9

Because np₀ (1-p₀) = 18.9 is > 10, the sample size is less than 5% of the population size and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied.

Hypothesis:

$\small \\ H_0 : p \leq 0.91 \\ H_a : p >0.91$

Here

P = 214 231 0.92641 n

Test statistic,

$\small \\ z = \frac{\hat{p} - P_0}{\sqrt{\frac{P_0 (1-P_0)}{n}}} \\ \\ \\ z = \frac{0.92641 - 0.91}{\sqrt{\frac{0.91(0.09)}{231}}} \\ \\ \\ z= 0.87$

p-value = P(z > 0.87) = 1-P(z < 0.87) = 0.192

Since p-value > $\small \alpha$ , do not reject the null hypothesis and conclude that there is not sufficient evidence that more 91% of patients taking drug are healed within 8 weeks.