Question

a random sample of 836 births included 430 boys. use a 0.05 significance level to test the claim that 50.5% of newborn babies are boys. do the results supp the belief that 50.5% of newborn babies are boys?
c. ( h_{0}: p
eq 0.505 )( h_{1}: p = 0.505 )
d. ( h_{0}: p = 0.505 )( h_{1}: p > 0.505 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is 52(round to two decimal places as needed)
identify the p - value for this hypothesis test.
the p - value for this hypothesis test is 0.603(round to three decimal places as needed)
identify the conclusion for this hypothesis test.
a. reject ( h_{0} ). there is sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys.
b. reject ( h_{0} ). there is not sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys.
c. fail to reject ( h_{0} ). there is not sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys.
d. fail to reject ( h_{0} ). there is sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys.
do the results support the belief that 50.5% of newborn babies are boys?
a. the results support the belief that 50.5% of newborn babies are boys because there was sufficient evidence to show that the belief is true.
b. the results do not support the belief that 50.5% of newborn babies are boys; the results merely show that there is not strong evidence against the rate of 50.5%.
c. the results do not support the belief that 50.5% of newborn babies are boys because there was sufficient evidence to show that the belief is untrue.
d. the results support the belief that 50.5% of newborn babies are boys because there was no evidence to show that the belief is untrue.

Explanation:

Step1: Hypothesis Testing Rule

In hypothesis testing, if the P - value is greater than the significance level ($\alpha$), we fail to reject the null hypothesis ($H_0$). Here, $\alpha = 0.05$ and the P - value is $0.603$.
Since $0.603>0.05$.

Step2: Conclusion

When we fail to reject $H_0$, it means there is not sufficient evidence to warrant rejection of the claim in the null hypothesis. The null hypothesis $H_0:p = 0.505$ (the claim that 50.5% of newborn babies are boys).

For the second part, failing to reject the null hypothesis does not prove the null hypothesis is true. It just means there is not strong evidence against it.

Answer:

For the hypothesis test conclusion: C. Fail to reject $H_0$. There is not sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys.
For whether the results support the belief: B. The results do not support the belief that 50.5% of newborn babies are boys; the results merely show that there is not strong evidence against the rate of 50.5%.