Question

4. A random sample of 860 births at St. Jude’s Hospital included 426 boys. The national proportion of newborn boy babies is 51.2%. Use a 0.01 significance level to test the claim that the proportion of newborn boy babies at this hospital is different than the national average.

a. Draw a normal curve for the sampling distribution for samples of size 860 births. Label the mean and the values for one, two and three standard deviations above and below the mean.

b. Construct a hypothesis test using a significance level of α=0.01. Be sure to show all your calculations, including your test statistic and your calculated P-value. Be sure to clearly argue your conclusion.

i. Is this problem about means or proportions?

ii. What is the most appropriate test, a two-tailed test, a right-tailed test, or a left- tailed test?

iii. What is your null hypothesis? iv. What is your alternative hypothesis? v. What is the value of the test statistic? Please mark the test statistic on your normal curve.

vi. What is the P-value?

vii. What is your decision? Do you reject or not reject ?0?

viii. What is your conclusion? (What does your decision translate to in words? To write your conclusion, please use the conclusion language that was discussed in class.)

c. Construct a 95% confidence interval for the given sample.

Answer 1