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 = -3.085926472
p = 0.0010145050
p = 0.0602836879
n = 282
a. is the test two-tailed, left-tailed, or right-tailed?
two-tailed test
left-tailed test
right-tailed test
b. what is the test statistic?
z =
(round to two decimal places as needed.)
c. what is the p-value?
p-value =
(round to four decimal places as needed.)

Explanation:

Step1: Determine the type of test

The claim is that less than 12% of treated subjects experienced headaches. In hypothesis testing, when the alternative hypothesis is of the form \(H_1:p < p_0\) (where \(p_0 = 0.12\) in this case), the test is left - tailed.

Step2: Identify the test statistic

From the calculator display, the value of \(z=-3.09\) (rounded to two decimal places).

Step3: Identify the P - value

From the calculator display, the value of \(p = 0.0010\) (rounded to four decimal places).

Answer:

a. Left - tailed test
b. \(z=-3.09\)
c. \(P - value = 0.0010\)