A certain drug is used to treat asthma. In a clinical trial of the drug, 23 of 250 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 8% 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<0.08 z=0.699378606 p=0.7578422729 ^p=0.0920000000 n=250 a. Is the test two-tailed, left-tailed, or right-tailed? b. What is the test statistic? c. What is the P-value? d. What is the null hypothesis, and what do you conclude about it? Decide whether to reject the null hypothesis. What is the final conclusion?
The following information is provided: The sample size is n=250, the number of favorable cases is x=23, and the sample proportion is p = 23/250 = 0.092, and the significance level is α=0.01.
Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: p = 0.08
Ha: p < 0.08
This corresponds to a left-tailed test, for which a z-test for one population proportion needs to be used.
The z-statistic is computed as follows:
Corresponding to Z = 0.699 , t he p-value is p=0.7578
Since p=0.7578≥0.01, it is concluded that the null hypothesis is not rejected.
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