Question

a random sample of 857 births included 427 boys. use a 0.01 significance level to test the claim that 51.1% of newbor babies are boys. do the results support the belief that 51.1% of newborn babies are boys?
c ( h_{0}: p
eq 0.511 )
( h_{1}: p = 0.511 )
d. ( h_{0}: p = 0.511 )
( h_{1}: p
eq 0.511 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is ( -0.76 )
(round to two decimal places as needed.)
identify the p-value for this hypothesis test.
the p-value for this hypothesis test is ( square )
(round to three decimal places as needed)

Explanation:

Step1: Determine the type of test

This is a two - tailed test since \(H_1:p
eq0.511\).

Step2: Use the formula for the P - value in a two - tailed z - test

The formula for the P - value in a two - tailed z - test is \(P - value = 2\times(1 - \Phi(|z|))\), where \(z=- 0.76\) and \(\Phi\) is the cumulative distribution function of the standard normal distribution.
First, find \(\Phi(0.76)\). Looking up in the standard normal table or using a calculator, \(\Phi(0.76)\approx0.7764\).
Then, \(P - value=2\times(1 - 0.7764)\)

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Answer:

The P - value for this hypothesis test is \(0.447\)