Question

Hormone Therapy and Dementia. An issue of Science News (Vol. $163$, No, $22$, pp. $341$-$342$) reported that the Women's Health Initiative cast doubts on the benefit of hormone-replacement therapy. Researchers randomly divided $4532$healthy women over the age of $65$years into two groups. One group, consisting of $2229$women, received hormone-replacement therapy; the other group, consisting of $2303$women, received a placebo. Over $5$years. $40$of the women receiving the hormone-replacement therapy were diagnosed with dementia, compared with $21$of those getting placebo.

1. At the $5\%$significance level, do the data provide sufficient evidence to conclude that healthy women over $65$\

years old who take hormone-replacement therapy are at greater risk for dementia than those who do not?

Short answer

1. The data provide sufficient evidence to conclude that healthy women over years old who take hormone replacement therapy are at greater risk for dementia than those who do not.

Step-by-step solution

Part a; Step 1: Given information

The given values are,$x_1=40,n_1=2229,x_2=21,n_2=2303,\alpha =0.05.$