Question

A random sample of 821 births included 430 boys. Use a 0.01 significance level to test the claim that 51.1% of newborn babies are boys. Do the results support the belief that 51.1% of newborn babies are boys? Identify the test statistic for this hypothesis test.

Answer 1

Solution :

Given that,

= 0.511

1 - = 0.489

n = 821

x = 430

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 430 / 821= 0.524

This a two tailed test.

Ho: p = 0.511

Ha: p 0.511

Test statistics

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

= ( 0.524 - 0.511) / (0.511*0.489) / 821

= 0.731

p-value = 2* P(Z > z )

= 2* ( 1 - P(Z < 0.731))

= 2 * ( 1 - 0.7676)

= 2* 0.2324

= 0.4648

The p-value is p = 0.4648, and since p = 0.4648 > 0.01, it is concluded that the null hypothesis is fails to rejected.

Conclusion :

It is concluded that the null hypothesis Ho is fails to rejected. Therefore, there is not enough evidence to claim that the

population proportion p is different than   , at the 0.01 significance level

​