Question

A pharmaceutical company claims that one of its drugs works on 90% of those who have a certain ailment. An experimenter, suspicious that the company is overexaggerating the drug's efficacy, decides to collect data to test the pharmaceutical company's claim to see if the true efficacy might be less. Of the 250 individuals surveyed, 215 individuals said the drug helped their ailment.
a. What is the null hypothesis?
b. What is the Z-value?
c. Based on an alpha of .10, should we reject or fail to reject the test?
d. What is the result of finding a z-statistic that is more extreme than the critical value?

Answer 1

Answer:

Below is the solution to the given points:

Step-by-step explanation:

Please find the complete question in the attached file.

For point a:

$H_0 : p \geq 0.90$

For point b:

$z=\frac{\frac{x}{n}-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{\frac{215}{250}-0.90}{\sqrt{\frac{0.9 \times 0.10 }{250}}}= -2.11$

For point c:

$Z_{critical} =z_{\alpha}=-1.28$

since the test statistics $< Z_{critical}$

Reject $H_o$

For point d:

$P(|z \leq -2.11|)=0.0174$