Question

A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this​ writing, 962 babies were born to parents using the new​ method, and 863 of them were girls. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution.

What is the test statistic? (round to two decimals)

What is the P-value? (round to three decimals as needed)

What is the conclusion?

Answer 1

Solution:

Given: A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl.

As of this​ writing, 962 babies were born to parents using the new​ method, and 863 of them were girls

That is:

Sample size = n = 962

x = number of girls born = 863

Thus sample proportion of girls born in a sample =

At 0.01 level of significance , we have to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl.

That is we have to test : p > 0.5

Part a) Identify the null​ hypothesis and alternative​ hypothesis:

the null​ hypothesis is:
H0: p = 0.5

the alternative​ hypothesis is:

H1: p > 0.5

Part b) What is the test statistic?

Since n = 962 is large sample size and

n*p = 962*0.5 = 481 > 10

n*(1-p) = 962*(1-0.5) = 962*0.5 = 481 > 10

Thus we can use the normal distribution as an approximation to the binomial distribution.

Thus find z test statistic:

Part c) What is the P-value?

P-value = P( Z > z test statistic value)

P-value = P( Z > 24.63)

Since z= 24.63 is very large z value and area above z = 24.63 is approximately 0.

Thus

P-value = 0.000

We can use excel command:

=1-NORM.S.DIST( 24.63 , TRUE)

=0.000

Part d) conclusion about the null​ hypothesis

Since P-value = 0.000 < 0.01 level of significance , we reject null hypothesis H0.

Part e) final conclusion that addresses the original claim.

Since we have rejected null hypothesis H0, there is sufficient evidence to support the claim that: the new method is effective in increasing the likelihood that a baby will be a girl.