Question

A certain drug is used to treat asthma. In a clinical trial of the? drug, 26 of 284 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 9?% 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? (e) below. a. two tailed, right tailed or left tailed? b. z=??? c. P value? d. null hypothesis e. final conclusion

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.09
Alternative hypothesis: P < 0.09

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.01698
z = (p - P) / S.D

z = 0.09

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than 0.09.

Thus, the P-value = 0.536

Interpret results. Since the P-value (0.536) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that less than 9?% of treated subjects experienced headaches.