Question

a random sample of 875 births included 427 boys. use a 0.10 significance level to test the claim that 51.3% of newborn babies are boys. do the results support the belief that 51.3\\% of newborn babies are boys? (round to two decimal places as needed.) identify the p - value for this hypothesis test. the p - value for this hypothesis test is 0.139. (round to three decimal places as needed.) identify the conclusion for this hypothesis test.
a. reject $h_0$. there is not sufficient evidence to warrant rejection of the claim that 51.3\\% of newborn babies are boys.
b. fail to reject $h_0$. there is sufficient evidence to warrant rejection of the claim that 51.3\\% of newborn babies are boys.
c. fail to reject $h_0$. there is not sufficient evidence to warrant rejection of the claim that 51.3\\% of newborn babies are boys.
d. reject $h_0$. there is sufficient evidence to warrant rejection of the claim that 51.3\\% of newborn babies are boys.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value\geq\alpha\), we fail to reject \(H_0\). Here, \(\alpha = 0.10\) and \(P - value=0.139\)

Step2: Compare the P - value and significance level

Since \(0.139>0.10\) (i.e., \(P - value>\alpha\))

Answer:

C. Fail to reject \(H_0\). There is not sufficient evidence to warrant rejection of the claim that \(51.3\%\) of newborn babies are boys.