Question

You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 38. Find the critical value that corresponds to a confidence level of 95%.

Answer 1

Answer: 1.96

Explanation:

We assume that the given population to have a normal distribution.

Given : Sample size : n=38 , since its greater than 30 , so the test applied here is z-test ( otherwise we use t-test for sample size less than 30).

Confidence level :
`0.95`

Then Significance level :
`\alpha=1-0.95=0.05`

The critical value we need for confidence interval is given by :_

`z_(\alpha/2)=z_(0.05/2)=z_(0.025)`

From the standard normal distribution table , the value of
`z_(0.025)=1.96`

Hence, the critical value that corresponds to a confidence level of 95% = 1.96