Question

A simple random sample of 55 adults’ measurements of their red blood cell count (in cells per microliter) is obtained. For the sample the mean is 5.28 and its standard deviation is 0.55. (i) Use a .01 significance level to test the claim that the sample is from a population with mean less than 5.37. (ii) Use a confidence interval to test the same claim.

Answer 1

(i)

n = 55

= 5.28

s = 0.55

SE = s/

= 0.55/

= 0.0742

= 0.01

ndf = n - 1 = 55 - 1 = 54

From Table, critical values of t = 2.6700

Confidence Interval:

5.28 (2.6700 X 0.0742)

= 5.28 0.1980

= ( 5.0820 ,5.4780)

Confidence Interval:

5.0820 < <   5.4780

(ii)

Since not all the values of the Confidence Interval 5.0820 < <   5.4780 are less than 5.37, we conclude that the sample is not from a population with mean less than 5.37.