Question

A random sample of 857 births included 434 boys. Use a 0.10 significance level to test the claim that 51.4​% of newborn babies are boys. Do the results support the belief that 51.4​% of newborn babies are​ boys?

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

Choose the correct answer below.

A. Upper H 0​: pnot equals0.514 Upper H 1​: pequals0.514

B. Upper H 0​: pequals0.514 Upper H 1​: pgreater than0.514

C. Upper H 0​: pequals0.514 Upper H 1​: pnot equals0.514

D. Upper H 0​: pequals0.514 Upper H 1​: pless than0.514

Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is nothing. ​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test. The​ P-value for this hypothesis test is nothing. ​(Round to three decimal places as​ needed.)

Identify the conclusion for this hypothesis test.

A. Reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that 51.4​% of newborn babies are boys.

B. Fail to reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that 51.4​% of newborn babies are boys.

C. Fail to reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that 51.4​% of newborn babies are boys.

D. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that 51.4​% of newborn babies are boys.

Do the results support the belief that 51.4​% of newborn babies are​ boys?

A. The results do not support the belief that 51.4​% of newborn babies are​ boys; the results merely show that there is not strong evidence against the rate of 51.4​%.

B. The results support the belief that 51.4​% of newborn babies are boys because there was no evidence to show that the belief is untrue.

C. The results support the belief that 51.4​% of newborn babies are boys because there was sufficient evidence to show that the belief is true. D. The results do not support the belief that 51.4​% of newborn babies are boys because there was sufficient evidence to show that the belief is untrue.

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses: Option C is correct.

Test statistic = -0.44

P - value = 0.657

Conclusion: Option C is correct.

Last part: The results support the belief that 51.4​% of newborn babies are boys because there was no evidence to show that the belief is untrue.