Question

A researcher has collected the blood samples of 30 individuals and found that the mean hemoglobin concentration for the sample of individuals is 13.9 grams per deciliter and the standard deviation is 1.43 grams per deciliter. Calculate a 99.0% confidence interval for the mean hemoglobin concentration for the population.

[1] (10.22, 17.58)

[2] (13.17, 14.63)

[3] (13.18, 14.62)

[4] (13.23, 14.57)

Answer 1

Solution :

Given that,

= 13.9

s = 1.43

n = 30

Degrees of freedom = df = n - 1 = 30 - 1 = 29

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,29 =2.756

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

= 2.756 * (1.43 / 30)

= 0.72

Margin of error = 0.72

The 99% confidence interval estimate of the population mean is,

- E < < + E

13.9 - 0.72 < < 13.9 + 0.72

13.18 < < 14.62

Option (13.18, 14.62 ) is correct.