Question

a random sample of 836 births included 430 boys. use a 0.05 significance level to test the claim that 50.5% of newborn babies are boys. do the results support the belief that 50.5% of newborn babies are boys? identify the null and alternative hypotheses for this test. choose the correct answer below. a. $h_{0}: p = 0.505$ $h_{1}: p
eq 0.505$ b. $h_{0}: p = 0.505$ $h_{1}: p < 0.505$ c. $h_{0}: p
eq 0.505$ $h_{1}: p = 0.505$ d. $h_{0}: p = 0.505$ $h_{1}: p > 0.505$ identify the test statistic for this hypothesis test. the test statistic for this hypothesis test is 52 (round to two decimal places as needed.) identify the p - value for this hypothesis test. the p - value for this hypothesis test is 0.603 (round to three decimal places as needed.) identify the conclusion for this hypothesis test. a. reject $h_{0}$. there is sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys. b. reject $h_{0}$. there is not sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys. c. fail to reject $h_{0}$. there is not sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys. d. fail to reject $h_{0}$. there is sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys.

Explanation:

Step1: Determine the hypothesis

The null hypothesis \(H_0\) is the claim being tested. Here, the claim is \(p = 0.505\). The alternative hypothesis \(H_1\) for a two - tailed test (since we are just testing if the proportion is different) is \(p
eq0.505\).

Step2: Analyze the P - value

We are given a significance level \(\alpha=0.05\). If the P - value is greater than \(\alpha\), we fail to reject the null hypothesis. The P - value is \(0.603\) and \(0.603>0.05\)

Answer:

C. Fail to reject \(H_0\). There is not sufficient evidence to warrant rejection of the claim that \(50.5\%\) of newborn babies are boys.