Question

A random sample of 837 births included 425 boys. Use a 0.10 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?

a.) Test statistic:

b.) p-value:

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.512

Ha : p 0.512

n = 837

x = 425

= x / n = 425 / 837 =0.508

P0 = 0.512

1 - P0 = 1 - 0.512 =0.488

a ) Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.508 -0.512 / [(0.512 * 0.488) / 837 ]

= -0.24

Test statistic = z = -0.24

b ) P(z < -0.24 ) = 0.4052

P-value = 2 *0.4052 = 0.8104

= 0.10

P-value >

0.8104 > 0.10

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that