Question

A random sample of 862 births included 434 boys. Use a 0.10 significance level to test the claim that 50.7​%

of newborn babies are boys. Do the results support the belief that 50.7​%

of newborn babies are​ boys? Identify the test statistic for this hypothesis test. Identify the​ P-value for this hypothesis test. Identify the conclusion for this hypothesis test.

Answer 1

Let = The Proportion of newborn babies that are boys = 434 / 862 = 0.5035

Let p = The Population proportion of newborn babies that are boys = 50.7% = 0.507

1 - p = 0.493

= 0.10

The Hypothesis:

H0: p = 0.507: The proportion of newborn babies that are boys is equal to 0.507.

Ha: p 0.507: The proportion of newborn babies that are boys is different from 0.507.

This is a 2 Tailed Test.

The Test Statistic: We use the z test as

(i) This is a simple random sample

(ii) The samples are independent and

(iii) n * p and n * (1 - p) are both 10

The p Value: The p value (2 Tail) for Z = -0.21, is; p value = 0.8336

The Decision Rule: The p value Method: If the P value is < , Then Reject H0

The Decision: The p value Method: Since P value (0.8336) is > (0.10), We Fail to Reject H0.

The Conclusion: There is insufficient evidence at the 90% significance level to conclude that the proportion of newborn babies that are boys is different from 0.507.