Question

# A random sample of 857 births included 429 boys. Use a 0.10 significance level to test...

A random sample of 857 births included 429 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? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0​: pequals0.512 Upper H 1​: pnot equals0.512 B. Upper H 0​: pequals0.512 Upper H 1​: pgreater than0.512 C. Upper H 0​: pequals0.512 Upper H 1​: pless than0.512 D. Upper H 0​: pnot equals0.512 Upper H 1​: pequals0.512 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is nothing. ​(Round to two decimal places as​ needed.) Identify the​ P-value for this hypothesis test. The​ P-value for this hypothesis test is nothing. ​(Round to three decimal places as​ needed.)

Solution :

Given that,

= 0.512

1 - = 0.488

n = 857

x = 429

Level of significance = = 0.10

Point estimate = sample proportion = = x / n = 0.501

This a two tailed test.

A)

Ho: p = 0.512

Ha: p 0.512

Test statistics

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

= ( 0.501 - 0.512) / (0.512*0.488) / 857

= -0.67

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

= 2* P(Z < -0.67)

= 1 - 0.2514

= 0.503

The p-value is p = 0.503, and since p = 0.503 > 0.10, it is concluded that the null hypothesis is fails to rejected.