Question

A clinical trial was conducted using a new method designed to increase the probability of conceiving a boy. As of this? writing, 281 babies were born to parents using the new? method, and 243 of them were boys. Use a 0.05 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a boy. 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. How do you find the P value using a TI-84 calculator?

Answer 1

Let p denotes the proportion of boys in the new method.

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

The value of the test statistic

P-value

Since P-value = 0 < 0.05, so we reject H₀ at 5% level of significance and we can conclude that  new method significantly increased the probability of conceiving a boy.