Question

In the state of New York, a sample of 25 pregnant mothers takes a vitamin supplement. For this sample, the mean birth weight of the babies is 7.9 pounds with a standard deviation of 1.45 pounds. Find the 95% confidence interval for m - the mean birth weight for all babies whose mothers take the supplement . State the lower, upper limits for the interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 7.9

sample standard deviation = s = 1.45

sample size = n = 25

Degrees of freedom = df = n - 1 = 0.24

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,24 = 2.064

Margin of error = E = t_/2,df * (s /n)

= 2.064* (1.45 / 25)

= 0.6

The 95% confidence interval estimate of the population mean is,

- E < < + E

7.9 - 0.6 < < 7.9 +0.6

7.3 < < 8.5

(7.3, 8.5 )