Question

a random sample of 875 births included 427 boys. use a 0.10 significance level to test the claim that 51.3% of babies are boys. do the results support the belief that 51.3% of newborn babies are boys?

b. ( h_{0}: p = 0.513 )
( h_{1}: p>0.513 )
c. ( h_{0}: p
eq0.513 )
( h_{1}: p = 0.513 )
d. ( h_{0}: p = 0.513 )
( h_{1}: p
eq0.513 )

identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is ( -1.48 ).
(round to two decimal places as needed.)

identify the p - value for this hypothesis test.
the p - value for this hypothesis test is
(round to three decimal places as needed.)

Explanation:

Step1: Determine the type of test

This is a two - tailed test (since \(H_1:p
eq0.513\)). For a two - tailed z - test, the P - value is \(2\times(1 - \Phi(|z|))\), where \(z=- 1.48\) is the test statistic and \(\Phi(z)\) is the cumulative distribution function of the standard normal distribution.

Step2: Calculate the P - value

We know that for \(z = 1.48\), using a standard normal table or a calculator with a normal distribution function (e.g., in Excel: =NORM.S.DIST(1.48,TRUE)), \(\Phi(1.48)=0.9306\). Then \(1-\Phi(1.48)=1 - 0.9306=0.0694\). Since it is a two - tailed test, \(P - value=2\times0.0694 = 0.139\)

Answer:

\(0.139\)