Question

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 18 of 283 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 11​% 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. ​

1-PropZTest

prop < 0.11

z = -2.494480782

p = 0.0063070779

ModifyingAbove p with caret = 0.0636042403

n = 283

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

b. What is the test​ statistic? zequals nothing ​(Round to two decimal places as​ needed.)

c. What is the​ P-value? ​P-valueequals nothing ​(Round to four decimal places as​ needed.)

d. What is the null​ hypothesis, and what do you conclude about​ it? Identify the null hypothesis. A. Upper H 0 : p less than 0.11 B. Upper H 0 : p equals 0.11 C. Upper H 0 : p greater than 0.11 D. Upper H 0 : p not equals 0.11

Decide whether to reject the null hypothesis. Choose the correct answer below. A. Fail to reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, alpha. B. Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, alpha. C. Reject the null hypothesis because the​ P-value is greater than the significance​ level, alpha. D. Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, alpha. e.

What is the final​ conclusion? A. There is sufficient evidence to support the claim that less than 11​% of treated subjects experienced headaches. B. There is not sufficient evidence to support the claim that less than 11​% of treated subjects experienced headaches. C. There is not sufficient evidence to warrant rejection of the claim that less than 11​% of treated subjects experienced headaches. D. There is sufficient evidence to warrant rejection of the claim that less than 11​% of treated subjects experienced headaches.

Answer 1

Solution:
Claim is The accompanying calculator display shows results from a test of the claim that less than 11​% of treated subjects experienced headaches, So null and alternate hypothesis can be written as follows:
Null hypothesis H0: p = 0.11
Alternate hypothesis Ha: p<0.11
Solution(a)
This one tailed and left tailed test
Solution(b)
Sample size = 283
Sample proportion p^ = 18/283
So Z test statistic can be calculated as
Z test statistic = (p^ - p)/sqrt(p*(1-p)/n) = ((18/283)-0.11)/sqrt(0.11*(1-0.11)/283) = -2.494480782
Solution(c)
As this is left tailed test so from Z table we found p-value = 0.0063
Solution(d)
So at alpha = 0.05, we can reject the null hypothesis as p-value is less than alpha value(0.0063<0.05) so its answer is B.
So we can say that there is sufficient evidence to support the claim that The accompanying calculator display shows results from a test of the claim that less than 11​% of treated subjects experienced headaches. So its correct answer is A.