Question

The waist sizes were measured for a random sample of individuals taken from a certain population, and they are (in inches):

40, 36, 42, 37, 39, 41

If one wishes to construct a 95% confidence interval estimate for the mean of the sampled population and the normality assumption is accepted, which of the followings is the correct estimate? (Choose the one that is closest to your answer.)

Answer 1

Since we are assuming the data is normally distributed, we use the z distribution for determing the confidence interval.

Confidence interval would be

where is the sample mean.

is the standard deviation

z is the z score

n is the sample size

For the given sample

n = 6

Standard deviation (s)=

s = 2.32

At significance level of 95%, alpha = 0.025

Using the z table, we get a z score of 1.96

Thus

Confidence interval =

= 37.27 and 40.97

Thus 95% Confidence interval for the mean of the sampled population lies between 37.27 and 40.97