Question

A random sample of 880 births included 433 boys. Use a 0.10 significance level to test the claim that 50.8% of newborn babies are boys. Do the results support the belief that 50.8% of newborn babies are​ boys?

Answer 1

Solution :

Given that,

= 0.508

1 - = 0.492

n = 880

x = 433

Level of significance = = 0.10

Point estimate = sample proportion = = x / n = 0.492

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.508

Ha: p 0.508

Test statistics

z = ( - ) / *(1-) / n

= ( 0.492 - 0.508) / (0.508*0.492) / 880

= -0.947

P-value = 2 * P(Z < z )

= 2 * P(Z < -0.947)

= 2 * 0.1718

= 0.3436

Since, P-value > 0.10. Fails to reject H0.

Conclusion:

It is concluded that the null hypothesis Ho is fail to rejected. Therefore, there is not enough evidence to claim that 50.8% of newborn babies are boys. at the α = 0.10 significance level.