Question

a random sample of 868 births included 425 boys. use a 0.10 significance level to test the claim that 50.9% of newbc babies are boys. do the results support the belief that 50.9% of newborn babies are boys? identify the null and alternative hypotheses for this test. choose the correct answer below. a. $h_{0}: p = 0.509$ $h_{1}: p
eq 0.509$ b. $h_{0}: p = 0.509$ $h_{1}: p gt 0.509$ c. $h_{0}: p
eq 0.509$ $h_{1}: p = 0.509$ d. $h_{0}: p = 0.509$ $h_{1}: p lt 0.509$ identify the test statistic for this hypothesis test. the test statistic for this hypothesis test is (round to two decimal places as needed.)

Explanation:

Step1: Identify null and alternative hypotheses

The claim is that \(p = 0.509\). The null hypothesis \(H_0\) is the statement of equality, so \(H_0:p = 0.509\). The alternative hypothesis \(H_1\) for a two - tailed test (since the problem just asks if the proportion is 50.9% without specifying direction) is \(H_1:p
eq0.509\).

Step2: Calculate the sample proportion \(\hat{p}\)

The sample proportion \(\hat{p}=\frac{x}{n}\), where \(x = 425\) (number of boys) and \(n=868\) (sample size). So \(\hat{p}=\frac{425}{868}\approx0.49\)

Step3: Calculate the test statistic \(z\)

The formula for the test statistic in a proportion test is \(z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}\)
Substitute \(p = 0.509\), \(\hat{p}=0.49\), and \(n = 868\)

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Answer:

A. \(H_0:p = 0.509\), \(H_1:p
eq0.509\)
The test statistic for this hypothesis test is \(-1.12\)