Question

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 23 of 265 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 10​% 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. 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. Choose the correct answer below. e. What is the final​ conclusion? 1-PropZTest prop < 0.1 z = -0.716677636 p = 0.2367865141 p = 0.0867924528 n = 265

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.1

H_a : p < 0.1

= x / n = 23 / 265 = 0.0868

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0868 - 0.1 / [(0.1 * 0.9) / 265]

= -0.717

P-value = 0.2368

= 0.05

P-value >

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that the accompanying calculator display shows results from a test of the claim that less than 10​% of treated subjects experienced headaches.