Question

A sample of 700 members has a mean 5.2 and variance 2.5. Find the 99% confidence interval for the mean.

Answer 1

Given:

A sample of 700 members has a mean 5.2 and variance 2.5.

To find:

Find the 99% confidence interval for the mean.

Solution:

From given, we have the data,

The sample of data = N = 700

Mean of the sample = M = 5.2

Variance of the sample = s² = 2.5

⇒ Standard deviation of the sample = s = √2.5 = 1.581

We use the below formula to find the 99% confidence interval,

μ = M ± Z(s)

where,

Z = Z statistic determined by confidence level

Now, we need to substitute the values in this formula to find the interval, so we have,

M = 5.2

Z = 2.58

s = √(1.5812/700) = 0.06

μ = M ± Z(s)

μ = 5.2 ± 2.58 × 0.06

μ = 5.2 ± 0.154