Question

A random sample of 854 births included 431 boys. Use a 0.05 significance level to test the claim that 51.4​% of newborn babies are boys. Do the results support the belief that 51.4​% of newborn babies are​ boys?

Identify the null and alternative hypotheses for this test. Identify the test statistic for this hypothesis test.

Identify the​ P-value for this hypothesis test.

Identify the conclusion for this hypothesis test.

Do the results support the belief that 51.4​% of newborn babies are​ boys?

Answer 1

A random sample of 854 births included 431 boys.

So here n= 854 and x = 431

Sample proportion of new born baby boys is  :

Claim : 51.4% of newborn babies are boys .

This is population proportion. And we need to test if it is true or not.

So the hypothesis are :

H0: P = 0.514 v/s H1: P 0.514

The test statistic is,

= -0.53

The p value is given by,

p value = 2* p ( z -0.53 )

We find p ( z -0.53 ) using excel formula " =norm.s.dist (-0.53,1) " .

So p ( z -0.53 ) = 0.2981

So p value = 2 * 0.2981 = 0.5962

We have level of significance = = 0.05

Conclusion :

So here p value > . Henc we failed to reject null hypothesis.

There are sufficient evidence to support that claim that 51.4​% of newborn babies are​ boys.