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 74 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 115 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 24 oz. At α = .04, 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?

(A) If the answer in (a) is greater than the answer in (c) then we cannot conclude at the 4% significance
level that the average birthweight from this hospital is different from the national average.

(B) If the answer in (b) is greater than the answer in (c) then we conclude at the 4% significance
level that the average birthweight from this hospital is different from the national average.

(C) If the answer in (a) is greater than the answer in (b) then we cannot conclude at the 4% significance
level that the average birthweight from this hospital is different from the national average

(D) If the answer in (c) is greater than 0.04 then we conclude at the 4% significance
level that the average birthweight from this hospital is different from the national average

(E) If the answer in (c) is less than 0.04 then we cannot conclude at the 4% significance
level that the average birthweight from this hospital is different from the national average

(F) If the answer in (c) is less than 0.04 then we conclude at the 4% significance
level that the average birthweight from this hospital is different from the national average.

(G) If the answer in (b) is greater than the answer in (c) then we cannot conclude at the 4% 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 (c) then we conclude at the 4% significance
level that the average birthweight from this hospital is different from the national average.

Answer 1

Result:

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 74 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 115 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 24 oz. At α = .04, can it be concluded that the average birthweight from this hospital is different from the national average? Find the value of the test statistic for the above hypothesis. Ho: µ = 120   H1: µ ≠ 120 = -1.7922 (b)       Find the critical value. critical z value at 0.04 level          =2.054 Reject Ho if calculated z < -2.054 or z > 2.054 (c)       Find the p-value. P value =         0.0731

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

Correct option: (F) If the answer in (c) is less than 0.04 then we conclude at the 4% significance
level that the average birthweight from this hospital is different from the national average.

Since calculated P value 0.0731 is > 0.04 the level of significance. Ho is not rejected.

There is not sufficient evidence to conclude that the average birthweight from this hospital is different from the national average of 120 oz.

Z Test of Hypothesis for the Mean
Data
Null Hypothesis                       m=	120
Level of Significance	0.04
Population Standard Deviation	24
Sample Size	74
Sample Mean	115
Intermediate Calculations
Standard Error of the Mean	2.7899
Z Test Statistic	-1.7922
Two-Tail Test
Lower Critical Value	-2.0537
Upper Critical Value	2.0537
p-Value	0.0731
Do not reject the null hypothesis