Question 1145710: In a clinical trial, 19 out of 885 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 1.8% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 1.8% of this drug's users experience flulike symptoms as a side effect at the α=0.01 level of significance?
A) Because np01−p0 =_____ ____ 10, the sample size is _____ 5% of the population size, and the sample __________________________________,the requirements for testing the hypothesis ______ satisfied.
(Round to one decimal place as needed.)
B) What are the null and alternative hypotheses?
H0:____ ____ _____ versus H1:____ ____ ____
(Type integers or decimals. Do not round.)
C) Find the test statistic, z 0
z0.= ______
(Round to two decimal places as needed.)
D) Find the P-value.
P-value= ________
(Round to three decimal places as needed.)
Choose the correct conclusion below.
A.
Since P-value>α, do not reject the null hypothesis and conclude that there is not sufficient evidence that more than1.9% of the users experience flulike symptoms.
B.
Since P-value>α,reject the null hypothesis and conclude that there is not sufficient evidence that more than 1.9% of the users experience flulike symptoms.
C.
Since P-value<α, do not reject the null hypothesis and conclude that there is sufficient evidence that more than 1.9% of the users experience flulike symptoms.
D.
Since P-value<α, reject the null hypothesis and conclude that there is sufficient evidence that more than 1.9% of the users experience flulike symptoms.
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Answer by andeeusry(1)   (Show Source):
You can put this solution on YOUR website! A) Because np, and n(1-p) _are both__greater than or equal to__ ____ 10, the sample size is __less than__ 5% of the population size, and the sample ____________can be reasonably assumed to be random_________,the requirements for testing the hypothesis ___are___ satisfied.
np, n(1-p) > = 10
np = 885*0.0215
= 19.0275
n(1-p) = 885*(1 - 0.0215)
= 865.9725
Hypotheses:
B) What are the null and alternative hypotheses?
H0: P = 0.018 versus H1: P > 0.018
C) Find the test statistic, z
n = 885
p-hat = 19/885
= 0.0215
P = 0.018
q = 1 - p
= 1 - 0.018
q = 0.982
Z = ( ( p-hat) - p )/√(p*q/n)
Z = ( 0.0215 - 0.018)/√( (0.018*0.982)/ 885 )
Z = 0.78
D) Find the P-value.
The area under the curve for z = 0.78 is 0.7823, Subtract the area from 1 to obtain the p-value,
p- value = 1 - 0.7823
p - value = 0.218
Since P-value>α, do not reject the null hypothesis and conclude that there is not sufficient evidence that more than1.8% of the users experience flulike symptoms.
Since P- value (0.218 ) > 0.01, we fail to reject the null hypothesis .
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