Question

A random sample of 15 people were taken from a normally distributed population, and the mean height of the population is going to be estimated with 95% confidence. What is the appropriate critical value that should be used to build the 95 confidence level?

Answer 1

a)

`z_(critical) \text{ at 0.05 level of significance } = \pm 1.96`

b)

`t_(critical) \text{ at 0.05 level of significance, 14 degree of freedom } = \pm 2.144`

Explanation:

We are given the following information in the question:

Sample size = 15

The population is normally distributed and the mean height of the population is going to be estimated with 95% confidence.

We have to find the appropriate critical value that should be used to build the 95 confidence level.

Confidence interval:

`\mu \pm \text{ critical value }(\sigma)/(√(n))`

If the population standard deviation is given, we use the z-critical value.

`z_(critical) \text{ at 0.05 level of significance } = \pm 1.96`

If the population standard deviation is not given, we use the t-critical value.

`t_(critical) \text{ at 0.05 level of significance, 14 degree of freedom } = \pm 2.144`