Question

Please work on the following hypothesis test question. It’s important that you make sure you know which situation you have before doing the hypothesis test.

A researcher believes that the proportion of men in nursing homes with Alzheimer’s is lower than the proportion of women. She collects a random sample of 100 men nursing home residents with 15 that have Alzheimer’s and a random sample of 100 women nursing home patients with 25 that have Alzheimer’s. Conduct a hypothesis test of the researcher’s claim at the 0.01 level of significance.    Make the 4 steps cleared as outlined on page 325 of your textbook

Answer 1

p1cap = X1/N1 = 15/100 = 0.15
p1cap = X2/N2 = 25/100 = 0.25
pcap = (X1 + X2)/(N1 + N2) = (15+25)/(100+100) = 0.2

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.15-0.25)/sqrt(0.2*(1-0.2)*(1/100 + 1/100))
z = -1.7678

P-value Approach
P-value = 0.0385
As P-value >= 0.01, fail to reject null hypothesis.

There is not significant evidence to conclude that the proportion of men in nursing homes with Alzheimer’s is lower than the proportion of women.