Question

a random sample of 870 births included 430 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?
the p - value for this hypothesis test is 0.203.
(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 51.3% of newborn babies are boys.
b. fail to reject ( h_0 ). there is not sufficient evidence to warrant rejection of the claim that 51.3% of newborn babies are boys.
c. reject ( h_0 ). there is not sufficient evidence to warrant rejection of the claim that 51.3% of newborn babies are boys.
d. fail to 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 the \(P - value>\alpha\) (significance level), we fail to reject \(H_0\). If \(P - value\leq\alpha\), we reject \(H_0\). Here, \(\alpha = 0.10\) and \(P - value=0.203\) (given).

Step2: Compare the \(P - value\) and \(\alpha\)

Since \(0.203>0.10\) (i.e., \(P - value>\alpha\)).

Answer:

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