Question

In the last few years, many research studies have shown that the purported benefits of hormone replacement therapy (HRT) do not exist, and in fact, that hormone replacement therapy actually increases the risk of several serious diseases. A four-year experiment involving 4544 women was conducted at 40 medical centres. 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 = 23 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. (Round your answers to two decimal places.)

3. Test statistic: z =

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2
p1cap = X1/N1 = 46/2272 = 0.0202
p1cap = X2/N2 = 23/2272 = 0.0101
pcap = (X1 + X2)/(N1 + N2) = (46+23)/(2272+2272) = 0.0152

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.0202-0.0101)/sqrt(0.0152*(1-0.0152)*(1/2272 + 1/2272))
z = 2.78

P-value Approach
P-value = 0.0027
As P-value < 0.01, reject the null hypothesis.