Question

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.)

Answer #1

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.

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