Question

In 1990 a national vital statistics report indicated that about 2.1% of all births produced twins. Is the rate of twin births the same among very young​ mothers? Data from a large city hospital found only 7 sets of twins were born to 531 teenage girls. Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Determine the​ z-test statistic. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

Find the​ P-value. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

What is your​ conclusion? Choose the correct answer below.

A.

Reject H0. The proportion of twin births for teenage mothers is greater than the proportion of twin births for all mothers.

B.

Reject H0. The proportion of twin births for teenage mothers is different from the proportion of twin births for all mothers.

C.

Fail to reject H0. The proportion of twin births for teenage mothers is not different from the proportion of twin births for all mothers.

D.

The assumptions and conditions are not​ met, so the test cannot proceed.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.021
Alternative Hypothesis: p ≠ 0.021

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.0132 - 0.021)/sqrt(0.021*(1-0.021)/531)
z = -1.25

P-value Approach
P-value = 0.2113
As P-value >= 0.05, fail to reject null hypothesis.

Fail to reject H0. The proportion of twin births for teenage mothers is not different from the proportion of twin births for all mothers.