Final answer:
a) The best point estimate of the prevalence rate p is 0.04.
b) An interval estimate of the parameter p can be obtained by using the formula for calculating a confidence interval for a proportion.
c) This interval estimate allows us to be 95% confident about the range in which the true prevalence rate of breast cancer lies.
Step-by-step explanation:
a) The best point estimate of the prevalence rate p is the proportion of women in the sample who had breast cancer.
This can be calculated by dividing the number of women with breast cancer (400) by the total number of women in the sample (10,000):
Point Estimate of p = 400/10,000 = 0.04
b) To obtain an interval estimate of the parameter p, we can use the formula for calculating a confidence interval for a proportion:
Interval Estimate = Point Estimate ± Margin of Error
The Margin of Error can be calculated using the formula:
Margin of Error = z * sqrt((Point Estimate * (1 - Point Estimate)) / n)
where z is the z-score corresponding to the desired level of confidence, sqrt represents the square root function, and n is the sample size.
c) The result can be interpreted as follows: We are 95% confident that the true prevalence rate of breast cancer among 50- to 54-year-old women whose mothers have had breast cancer is between the lower bound and the upper bound of the interval estimate.