Answer to Question #162923 in Quantitative Methods for Sunny

Question

When the population is not normally distributed, population variance is unknown and the sample size is 50, the confidence interval for the population mean is based on

a. the t- distribution with an unknown number of degrees of freedom

b. the t- distribution with 30 degrees of freedom

c. the F- distribution

d. The standard normal distribution

e. the binomial distribution.

Answer 1

Given,

Population is not distributed normally.

The population variance is unknown.

Sample size = 50

confidence interval for the population?

As per the central limit theorem, it states that the sampling distribution of the sample will approach a normal distribution as the sample size increases.

As per the general rule of thumb, the t- distribution with 30 degrees of freedom

$n\ge 30$