Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 18 of 295 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 0.01 significance level to complete parts (a) through (e) below.
1-propztest
prop < 0.12
z = -3.117498701
p = 0.0009119638
\\( \hat { p } = 0.0610169492 \\)
n = 295
a. is the test two-tailed, left-tailed, or right-tailed?
two-tailed test
right-tailed test
left-tailed test
b. what is the test statistic?
z = -3.12
(round to two decimal places as needed.)
c. what is the p-value?
p-value =
(round to three decimal places as needed.)

Explanation:

Step1: Recall the definition of P - value for a left - tailed test

For a left - tailed test with test statistic \(z\), the P - value is \(P(Z<z)\).

Step2: Use the standard normal distribution table or calculator

We know \(z=-3.12\). Using a standard normal distribution table (or a calculator with a normalcdf function for the left - tailed case: normalcdf\((-\infty,-3.12)\)), we find the probability.
From the standard normal table, \(P(Z < - 3.12)=0.0009\) (using more precise calculator values: if \(z=-3.117498701\) as in the display, \(P = 0.0009119638\))

Answer:

\(0.001\)