Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 17 of 282 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 12% of treated subjects experienced headaches. use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts (a) through (d) below.
1-propztest
prop < 0.12
z = -3.055926472
p = 0.0010145950
p = 0.0602836879
n = 282
c. h₀: p ≠ 0.12
d. h₀: p = 0.12
decide whether to reject the null hypothesis. choose the correct answer below.
a. fail to reject the null hypothesis because the p - value is less than or equal to the significance level, α.
b. fail to reject the null hypothesis because the p - value is greater than the significance level, α.
c. reject the null hypothesis because the p - value is less than or equal to the significance level, α.
d. reject the null hypothesis because the p - value is greater than the significance level, α.

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing, if the \(P -\)value \(\leq\alpha\) (significance level), we reject the null hypothesis \(H_0\). If the \(P -\)value\(>\alpha\), we fail to reject the null hypothesis \(H_0\). Here, the significance level \(\alpha = 0.05\) and from the calculator display, \(P=0.0010145950\).

Step2: Compare the \(P -\)value and \(\alpha\)

Since \(P = 0.0010145950\) and \(\alpha=0.05\), and \(0.0010145950<0.05\) (i.e., \(P -\)value \(\leq\alpha\)).

Answer:

C. Reject the null hypothesis because the \(P -\)value is less than or equal to the significance level, \(\alpha\)