A certain drug is used to treat asthma. In a clinical trial of the drug, 18 of 2

Question

A certain drug is used to treat asthma. In a clinical trial of the drug, 18 of 296 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 10.01 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? Identify the null hypothesis. Decide whether to reject the null hypothesis. Choose the correct answer below.

e. What is the final conclusion?

Explanation / Answer

Answers below:

a. This is the a left tailed test, because the hypothesis runs like this:

Since normal approximation is to be used. 10% of 296 = 29.6
Also, standard deviation = sqrt(npq) = sqrt(.1*.9*296) = 5.16

Ho: Mu>29.6
Ha: Mu<=29.6

The claim always comes in the alternative hypothesis.

b. the test statistic = t*
= (X-Mu)/Stdev  
= (18-29.6)/5.16
=-2.25

c. THe p-value is P(X<=-2.25) = .012

d. If .01 is our significance level, we fail to reject the null hypothesis ie.. Ho: Mu>29.6

In layman' language, the claim is not true. More than or equal to 10% of treated subjects experienced headaches

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