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

Step-by-step 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