Question

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 25 of 289 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.

A. Is the test two-tailed, left-tailed, or right-tailed?

B. What is the test statistic?

Z=[ ] (Round to TWO decimal places as needed)

C. What is the P-value?

P-value= [ ]    (Round to FOUR decimal places as needed)

D. What is the null hypotheses, and what do you conclude about it?

   Decide weather to reject the null hypothesis.

E. What is the final conclusion?

Answer 1

GIVEN:

Sample size of treated subjects

Number of treated subjects who experienced headaches​

HYPOTHESIS:

The hypothesis is given by,

(That is, the proportion of treated subjects who experienced headaches is equal to 8%.)

(That is, the proportion of treated subjects who experienced headaches is less than 8%.)

(A) The given test is LEFT TAILED TEST since alternative hypothesis is .

LEVEL OF SIGNIFICANCE:

(B) TEST STATISTIC:

which follows standard normal distribution.

where is the hypothesized value 0.08.

CALCULATION:

The sample proportion is given by,

  

The test statistic is,

  

  

(C) P VALUE:

The left tailed p value is given by,

From the z table, the probability value is the value with corresponding row 0.4 and column 0.04.

Thus the p value is .

DECISION RULE:

(D) Since the calculated p value (0.6700) is greater than the significance level , we fail to reject null hypothesis.

(E) CONCLUSION:

Since the calculated p value (0.6700) is greater than the significance level , we fail to reject null hypothesis and conclude that the proportion of treated subjects who experienced headaches is equal to 8%.