A certain drug is used to treat asthma. In a clinical trial of the drug, 29 of 280 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than $10 \%$ of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below.
\[
\begin{array}{l}
\text { 1-PropZTest } \\
\text { prop }< 0.1 \\
z=0.199204768 \\
p=0.5789487151 \\
\hat{p}=0.1035714286 \\
n=280
\end{array}
\]
c. What is the P-value?
P-value $=$
(Round to four decimal places as needed.)
d. What is the null hypothesis, and what do you conclude about it?
Identify the null hypothesis.
A. $H_{0}: p=0.1$
B. $H_{0}: p \neq 0.1$
Answer
Final Answer: The P-value is \(\boxed{0.5789}\) and the null hypothesis is \(\boxed{H_{0}: p=0.1}\).
Step 1 ：The P-value is given directly in the question as 0.5789487151. We round this to four decimal places to get \(0.5789\).
Step 2 ：The null hypothesis in a 1-PropZTest is always that the proportion is equal to a certain value. In this case, the value is 0.1. Therefore, the null hypothesis is \(H_{0}: p=0.1\).
Step 3 ：Final Answer: The P-value is \(\boxed{0.5789}\) and the null hypothesis is \(\boxed{H_{0}: p=0.1}\).
