Question

A 4-year experiment involving 4,346 women was conducted at 34 medical centers to study the benefits and risks of hormone replacement therapy (HRT). Half of the women took placebos and half took a prescription drug, a widely prescribed type of hormone replacement therapy. There were
x1 = 46
cases of dementia in the hormone group and
x2 = 22
in the placebo group. Is there sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug? Test at the 1% level of significance.

State the null and alternative hypotheses.
H0: (p1 ? p2) = 0 versus Ha: (p1 ? p2) < 0H0: (p1 ? p2) = 0 versus Ha: (p1 ? p2) ? 0    H0: (p1 ? p2) = 0 versus Ha: (p1 ? p2) > 0H0: (p1 ? p2) ? 0 versus Ha: (p1 ? p2) = 0H0: (p1 ? p2) < 0 versus Ha: (p1 ? p2) > 0
Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statistic     z =
rejection region     z >
    z <

State your conclusion.
H0 is not rejected. There is sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.H0 is not rejected. There is insufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.    H0 is rejected. There is sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.H0 is rejected. There is insufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.

Answer 1

A 4-year experiment involving 4,346 women was conducted at 34 medical centers to study the benefits and risks of hormone replacement therapy (HRT). Half of the women took a prescription drug, a widely prescribed type of hormone replacement therapy and hence and half took placebos that means for first group the number of women are . There were

cases of dementia in the hormone group and

in the placebo group.

So we want to test whether there is sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug at the 1% level of significance.

So in order to test that the null and alternative hypotheses be

where bethe population proportion of dementia with the drug and without thee drug

Now in order to test that the test statistic be,

where under Ho, Z~N(0,1)

and

So the value of the test statistic be,

since it is a right tailed test hencefor 0.01 level of sinificance the rejection region be,

rejection region:

As we see that hence our conclusion be,

H0 is rejected. There is sufficient evidence to indicate that the risk of dementia is higher for patients using the prescription drug.

Hence theanswer..........

Thank you.............