Question

Suppose that we want to test the hypothesis that mothers with low socioeconomic status (SES) deliver babies whose birthweights are different than "normal". To test this hypothesis, a list of birthweights from 91 consecutive, full-term, live-born deliveries from the maternity ward of a hospital in a low-SES area is obtained. The mean birghweight is found to be 118 oz. Suppose that we know from nationwide surveys based on millions of deliveries that the mean birthweight in the United States is 120 oz, with a standard deviation of 21 oz.

At α = .01, can it be concluded that the average birthweight from this hospital is different from the national average?

(a)	Find the value of the test statistic for the above hypothesis.

(b)	Find the critical value.

(c)	Find the p-value.

(d)	What is the correct way to draw a conclusion regarding the above hypothesis test?

options for d

(A) If the answer in (b) is greater than the answer in (c) then we cannot conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average. (B) If the answer in (c) is greater than 0.01 then we conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average. (C) If the answer in (c) is less than 0.01 then we cannot conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average. (D) If the answer in (b) is greater than the answer in (c) then we conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average. (E) If the answer in (a) is greater than the answer in (c) then we conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average. (F) If the answer in (a) is greater than the answer in (c) then we cannot conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average. (G) If the answer in (c) is less than 0.01 then we conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average. (H) If the answer in (a) is greater than the answer in (b) then we cannot conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average.

Answer 1

a) value of the test statistic = -0.909

b) critical value =2.576

c) e p-value =0.3634 (please try 0.3628 if this comes wrong)

d) . (G) If the answer in (c) is less than 0.01 then we conclude at the 1% significance
level that the average birthweight from this hospital is different from the national average.