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?identify the null and alternative hypotheses for this test. choose the correct answer below.o a. ( h_{0}: p = 0.513 )( h_{1}: p lt 0.513 )o b. ( h_{0}: p = 0.513 )( h_{1}: p gt 0.513 )o c. ( h_{0}: p
eq 0.513 )( h_{1}: p = 0.513 )o d. ( h_{0}: p = 0.513 )( h_{1}: p
eq 0.513 )

Explanation:

• The null hypothesis \(H_0\) is a statement of equality. Here, the claim is about a proportion \(p = 0.513\), so \(H_0:p = 0.513\).
• The alternative hypothesis \(H_1\) is the statement that we are trying to find evidence for. Since we are just testing if the proportion is different from \(0.513\) (a two - tailed test, as there is no prior indication of direction like “more than” or “less than” in the general claim “test the claim that \(51.3\%\) of newborn babies are boys”), \(H_1:p

eq0.513\).

Answer:

D. \(H_0: p = 0.513\), \(H_1: p
eq0.513\)