Question

A random sample of 836 births included 425 boys. Use a 0.01 significance level to test the claim that 51.2​% of newborn babies are boys. Do the results support the belief that 51.2​% of newborn babies are​ boys? Identify the null and alternative hypotheses for this test.

Answer 1

Let p denotes the proportion of boys among the newborn babies.

To test against

Here

sample proportion of boys among the newborn babies

and sample size n = 836

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 1% level of significance if

Now,

The value of the test statistic

and critical value

Since , so we fail to reject H₀ at 1% level of significance and we can conclude that there is not enough evidence to support the claim that 51.2​% of newborn babies are​ boys.