Question

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A certain drug is used to treat asthma. In a clinical trial of the drug. 27 of 285 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. peop<0.1 2-Prop Teas :-0.202302529 -0.5407724707 P-0.1012867925 a. Is the test two-tailed, left-tailed, or right-tailed? O Left-tailed test O Two-tailed test O Right tailed test b. What is the test statistic? (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 hypothesis and what do you conclude about it? Identify the null hypothesis O A. Ho: p=0.1 OB. Ho:p> 0.1 02. Hu: <0.1 OD. He: p=0.1 Decide whether to reject the null hypothesis. Choose the correct answer below. O A. Reject the null hypothesis because the P-value is greater than the significance level, a OB. Fail to reject the null hypothesis because the P-value is greater than the significance level, OC. Reject the null hypothesis because the P-value is less than or equal to the significance level, a OD. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, e. What is the final conclusion? O A. There is sufficient evidence to support the claim that less than 10% of treated subjects experienced headaches. OB. There is not sufficient evidence to support the claim that less than 10% of treated subjects experienced headaches OC. There is sufficient evidence to warrant rejection of the claim that less than 10% of treated subjects experienced headaches OD. There is not sufficient evidence to warrant rejection of the claim that less than 10% of treated subjects experienced headaches

Answer 1

Part a)

Left tailed test

Part b)

Test Statistic :-
Z = ( P - P0) / √(P0 * q0 / n)
Z = ( 0.1019 - 0.1 ) / √(( 0.1 * 0.9) /265)
Z = 0.10

Part c)

P value = P ( Z < 0.10 ) = 0.5408

Part d)

H0 :- P = 0.10

Reject null hypothesis if P value < α = 0.05
Since P value = 0.5408 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Option B is correct

Part e)

Option B is correct