Question

Rearrange each of the following inequalities so that zero is on the right-hand side.

a. p1< p2 b. p1> p2 c. p1/= p2 for C. the line goes through the equals sign.

Suppose the Acme Drug Company develops a new drug, designed to prevent
colds. The company states that the drug is equally effective for men and women.
To test this claim, they choose a random sample of 100 women and 100 men. At
the end of the study, 38% of the women caught a cold; and 51% of the men
caught a cold.
a. Define the appropriate parameter(s) and state the hypotheses for testing if
this study provides evidence that the drug is not equally effective for men
and women.
b. Set each of the hypotheses equal to zero and find the null value.

Answer 1

Given that,
sample one, x1 =38, n1 =100, p1= x1/n1=0.38
sample two, x2 =51, n2 =100, p2= x2/n2=0.51
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.38-0.51)/sqrt((0.445*0.555(1/100+1/100))
zo =-1.85
| zo | =1.85
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =1.85 & | z α | =1.96
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.8497 ) = 0.0644
hence value of p0.05 < 0.0644,here we do not reject Ho
ANSWERS
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b.
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: -1.85
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.0644
a.
we do not have enough evidence to support the claim that if
this study provides evidence that the drug is not equally effective for men
and women.