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 69 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 116 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 23 oz. At α = .06, 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.

Answer 1

Solution :

Given that,

= 116

= 120

= 23

n = 69

(a)

Test statistic = z = ( - ) / / n = (116 - 120) / 23 / 69 = -1.44

This is the two tailed test .

P(z < -1.4446) = 0.0749

P-value = 2 * P(z < -1.4446) = 2 * 0.0749 = 0.1498

= 0.06

P-value >

Fail to reject the null hypothesis

It can not be concluded that the average birthweight from this hospital

is different from the national average .

= 1 - 96% = 1 - 0.96 = 0.04

/ 2 = 0.04 / 2 = 0.02

Z_/2 = Z_0.02 = 2.05

Critical value =  2.05