Question

Plan B is the common name in the United States and Canada for the emergency contraception drug levonorgestrel. The high dose of progestogen it delivers has been shown in the lab to inhibit ovulation, thus rendering fertilization impossible. Some groups, however, are concerned that if the drug interfered with the fertilized egg, it could be considered abortive rather than strictly contraceptive. Researchers enrolled a cohort of fertile women attending a family planning clinic for emergency contraception after unprotected intercourse during their fertile period. From interviews, blood samples, and ultrasounds, the researchers were able to establish the time of intercourse relative to the women's menstrual cycles. In this cohort, 8787 women had unprotected intercourse before ovulation (pre‑ovulation group) and 3535 women had unprotected intercourse on or after ovulation (post‑ovulation group). Based on standard clinical assessments of fertility rates by day of the menstrual cycle, the researchers expected 13.313.3 pregnancies in the pre‑ovulation group and 7.07.0 pregnancies in the post‑ovulation group. Instead, they observed 00 and 66 pregnancies, respectively.

(a) We want to know if there is evidence that Plan B impacts the chance of pregnancy when taken before ovulation. What are the observed and expected counts of pregnancy and no pregnancy in the pre‑ovulation group? (Enter your answers rounded to one decimal place.)

Pregnancyobserved=Pregnancyobserved=

Pregnancyexpected=Pregnancyexpected=

No pregnancyobserved=No pregnancyobserved=

No pregnancyexpected=No pregnancyexpected=

Use these counts to compute the chi‑square statistic. (Enter your answer rounded to two decimal places.)

?2=χ2=

Select the correct response to whether or not the test assumptions met.

The expected counts are not large enough, so the test assumptions are not met.

A cohort can be considered a random sample and the expected counts are large enough, so the test assumptions are met.

A cohort cannot be considered a random sample, so the test assumptions are not met.

Neither the cohort can be considered a random sample nor the expected counts are large enough, so the test assumptions are not met.

Calculate the degrees of freedom. (Enter your answer as a whole number.)

df=df=

Find the ?P‑value. (Enter your answer rounded to six decimal places.)

?P‑value ==

Select the correct conclusion.

None of the options are correct.

There is very strong evidence that Plan B impacts the chance of pregnancy when taken before ovulation.

The study found weak evidence that Plan B impacts the chance of pregnancy when taken before ovulation.

The study failed to find evidence that Plan B impacts the chance of pregnancy when taken before ovulation.

(b) We want to know if there is evidence that plan B impacts the chance of pregnancy when taken after ovulation. What are the observed and expected counts of pregnancy and no pregnancy in the post‑ovulation group? (Enter your answer rounded to one decimal place.)

Pregnancyobserved=Pregnancyobserved=

Pregnancyexpected=Pregnancyexpected=

No pregnancyobserved=No pregnancyobserved=

No pregnancyexpected=No pregnancyexpected=

Use these counts to compute the chi‑square statistic. (Enter your answer rounded to two decimal places.)

?2=χ2=

Select the correct response to whether or not the test assumptions met.

A cohort can be considered a random sample and the expected counts are large enough, so the test assumptions are met.

Neither the cohort can be considered a random sample nor the expected counts are large enough, so the test assumptions are not met.

The expected counts are not large enough, so the test assumptions are not met.

A cohort cannot be considered a random sample, so the test assumptions are not met.

Calculate the degrees of freedom. (Enter your answer as a whole number.)

df=df=

Find the ?P‑value. (Enter your answer rounded to four decimal places.)

?P‑value ==

Select the correct conclusion.

The study failed to find evidence that Plan B impacts the chance of pregnancy when taken after ovulation.

None of the options are correct.

The study found weak evidence that Plan B impacts the chance of pregnancy when taken after ovulation.

There is strong evidence that Plan B impacts the chance of pregnancy when taken after ovulation.

(c) Select the correct description of the study findings and what they suggest about the mechanism of action of the Plan B drug.

There is no evidence that Plan B prevents pregnancy when taken before ovulation or after ovulation. These findings reject the theory that Plan B works by inhibiting ovulation.

There is very strong evidence that Plan B prevents pregnancy when taken after ovulation but not when taken before ovulation. These findings support the theory that Plan B works by inhibiting ovulation.

There is weak evidence that Plan B prevents pregnancy when taken before ovulation but not when taken after ovulation. These findings support the theory that Plan B works by inhibiting ovulation.

There is very strong evidence that Plan B prevents pregnancy when taken before ovulation but not when taken after ovulation. These findings support the theory that Plan B works by inhibiting ovulation.

Answer 1

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Answer:

(a)
Pregnancy(observed) = 0
Pregnancy(expected) = 13.3
NoPregnancy(observed) = 87 - 0 = 87
NoPregnancy(expected) = 87 - 13.3 = 73.7

= (0 - 13.3)² / 13.3 + (87 - 73.7)² / 73.7 = 15.700

The expected counts are greater than 5. So,
A cohort can be considered a random sample and the expected counts are large enough, so the test assumptions are met.

df = n-1 = 2-1 = 1

P-value = P( > 15.56, df = 1) = 0.000074

Since p-value is less than 0.05 significance level, we conclude that

There is very strong evidence that Plan B impacts the chance of pregnancy when taken before ovulation.

(b)

Pregnancy(observed) = 6
Pregnancy(expected) = 7.0
NoPregnancy(observed) = 35 - 6 = 29
NoPregnancy(expected) = 35 - 7.0 = 28

= (6 - 7.0)² / 7.0 + (29 - 28)² / 28 = 0.17857

The expected counts are greater than 5. So,
A cohort can be considered a random sample and the expected counts are large enough, so the test assumptions are met.

df = n-1 = 2-1 = 1

P-value = P( > 0.25, df = 1) = 0.6726

Since p-value is greater than 0.05 significance level, we conclude that

The study failed to find evidence that Plan B impacts the chance of pregnancy when taken after ovulation.

(c)
There is very strong evidence that Plan B prevents pregnancy when taken before ovulation but not when taken after ovulation. These findings support the theory that Plan B works by inhibiting ovulation.