Question

a random sample of 859 births included 426 boys. use a 0.01 significance level to test the claim that 50.6% of newborn babies are boys. do the results support the belief that 50.6% of newborn babies are boys?
identify the null and alternative hypotheses for this test. choose the correct answer below
oa. ( h_0: p = 0.506 )
( h_1: p < 0.506 )
ob. ( h_0: p = 0.506 )
( h_1: p > 0.506 )
oc. ( h_0: p
eq 0.506 )
( h_1: p = 0.506 )
od. ( h_0: p = 0.506 )
( h_1: p
eq 0.506 )

Explanation:

Step1: Understand null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The claim is that \(p = 0.506\). The alternative hypothesis \(H_1\) for a two - tailed test (since we are just testing if the proportion is different from the claimed value, not specifically greater or less) is \(p
eq0.506\).

Step2: Analyze each option

• Option A: \(H_1:p < 0.506\) is a left - tailed test. But the problem is not just claiming the proportion is less.
• Option B: \(H_1:p>0.506\) is a right - tailed test. But the problem is not just claiming the proportion is greater.
• Option C: The null and alternative hypotheses are reversed. \(H_0\) should be the statement of equality.
• Option D: \(H_0:p = 0.506\) (null hypothesis as the claim of equality) and \(H_1:p

eq0.506\) (two - tailed alternative hypothesis) is correct.

Answer:

D. \(H_0:p = 0.506\), \(H_1:p
eq0.506\)