Question

a random sample of 828 births included 427 boys. use a 0.01 significance level to test the claim that 50.9% of newborn babies are boys. do the results support the belief that 50.9% of newborn babies are boys? identify the null and alternative hypotheses for this test. choose the correct answer below. a. ( h_{0}: p = 0.509 ) ( h_{1}: p < 0.509 ) b. ( h_{0}: p = 0.509 ) ( h_{1}: p > 0.509 ) c. ( h_{0}: p
eq 0.509 ) ( h_{1}: p = 0.509 ) d. ( h_{0}: p = 0.509 ) ( h_{1}: p
eq 0.509 )

Explanation:

Step1: Understand the null and alternative hypotheses concepts

The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is a statement that contradicts \(H_0\).

Step2: Analyze each option

• Option A: \(H_1: p < 0.509\) is a one - sided (left - tailed) test. But the claim is about a specific proportion, not just less than.
• Option B: \(H_1: p>0.509\) is a one - sided (right - tailed) test. But the claim is not just greater than.
• Option C: \(H_0: p

eq0.509\) is incorrect as the null hypothesis should be the claim of equality first.

• Option D: \(H_0: p = 0.509\) (the claim is tested as the null hypothesis) and \(H_1: p

eq0.509\) (a two - tailed test which is appropriate when we are just testing if the proportion is different from the claimed value without a specific direction of less than or greater than).

Answer:

D. \(H_0: p = 0.509\), \(H_1: p
eq0.509\)