State null and alternative hypothesis of interest for this

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Suppose that a pharmaceutical company wants to claim that side effects will be experienced by fewer than 20% of the patients who use a particular medication. In a clinical trial with 400 patients, they find that 61 patients experienced side effects. Is there enough evidence to claim that less than 20% of the patients experience side effects? Test at a 1% significance level.

a) State null and alternative hypothesis of interest for this problem and compute the test statistic.

b) Compute the P-value associated with this test and discuss whether its value shows evidence against the null hypothesis in part (a).

(Use a significance level alpha = 0.01).

c) Determine the critical region for this test based on the level alpha = 0.01.

d) Construct a 99% confidence interval for the percentage of patients that experienced side effects. Is the confidence interval consistent with your conclusions from part (b)? Explain.

e) How many patients must be sampled to obtain a 99% confidence interval with a total width of less than 0.05?

Reference no: EM13625970

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