Question

a random sample of 857 births included 427 boys. use a 0.01 significance level to test the claim that 51.1% of newborn babies are boys. do the results support the belief that 51.1% of newborn babies are boys?
identify the null and alternative hypotheses for this test. choose the correct answer below.
○ a. ( h_0: p = 0.511 )
( h_1: p < 0.511 )
○ b. ( h_0: p = 0.511 )
( h_1: p > 0.511 )
○ c. ( h_0: p
eq 0.511 )
( h_1: p = 0.511 )
○ d. ( h_0: p = 0.511 )
( h_1: p
eq 0.511 )

Explanation:

Step1: Determine the null hypothesis

The null hypothesis \(H_0\) is a statement of equality. Here, the claim is about a proportion \(p\). Since the claim is “\(51.1\%\) of newborn babies are boys”, the null hypothesis is \(H_0:p = 0.511\).

Step2: Determine the alternative hypothesis

The alternative hypothesis \(H_1\) is the statement that contradicts the null hypothesis. When we are just testing if the proportion is different from the claimed value (not specifically greater or less), it is a two - tailed test. So \(H_1:p
eq0.511\)

Answer:

D. \(H_0:p = 0.511\), \(H_1:p
eq0.511\)