Pharmaceutical companies advertise that the birth control pill has an efficacy o

Question

Pharmaceutical companies advertise that the birth control pill has an efficacy of 99.5% in preventing

pregnancy. However, under typical use the real efficacy is only about 95%. That is, 5% of women

taking the pill for a year will experience an unplanned pregnancy that year.5 A gynecologist looks back

at a random sample of medical records of patients who were prescribed the pill one year ago.

(a)What are the mean and standard deviation of the distribution of sample proportions of women

experiencing unplanned pregnancies?

(b)The gynecologist takes an SRS of 200 records and finds that 14 women had become pregnant

within one year while taking the pill. How surprising is this finding? Give the probability of finding 7%

or more pregnant women in the sample.

(c)How surprising would it be if the gynecologist had found 16 pregnant women (8%)? 20 pregnant

women (10%)?

Please provide elaborate answer

Explanation / Answer

Pharmaceutical companies advertise that the birth control pill has an efficacy of 99.5% in preventing pregnancy.

under typical use the real efficacy is only about 95%.

That is, 5% of women taking the pill for a year will experience an unplanned pregnancy that year.

sample proportions of women experiencing unplanned pregnancies is 5%

n = 100 ,P=5% = 0.05

using binomial distribution,

Mean = n*p = 100 * 0.05 = 5

variance = n * p * (1 - p) = 100 * 0.05 * 0.95 = 4.75 = 5 rounded to nearest integer.

b)

The gynecologist takes an SRS of 200 records and finds that 14 women had become pregnant

within one year while taking the pill this result surprizes because out of 200 more than 5%

women become pregnant within one year while taking the pill.

probability of finding = x / n = 14 / 200 = 0.07 = 7%

if the gynecologist had found 16 pregnant women (8%) i.e. more than 5% and 20 pregnant women (10%) it surprizes because it is greater than the 5% of women taking the pill for a year will experience an unplanned pregnancy that year which is larger than the real efficacy.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.