Question

Assuming the random variable X is normally distributed, compute the lower limit of the 95% confidence interval for the population mean if a random sample of size n=11 produces a sample mean of 38 and sample standard deviation of 5.2.
Round to two decimals.

Answer 1

Sample size = n = 11

Sample mean = = 38

Standard deviation = s = 5.2

We have to construct 95% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 11 - 1 = 10

Level of significance = 0.05

tc = 2.228   ( Using t table)

So confidence interval is ( 38 - 3.4934 , 38 + 3.4934) = > ( 34.51 , 41.49)

The lower limit of the 95% confidence interval for the population mean = 34.51