Question

A random of 25 observations was drawn from a normal population. The sample mean and the sample standard deviation are 52 and 15 accordingly. Is there enough evidence at 10% significance level to infer that the population mean is not equal to 50? Estimate the population mean as well.

Answer 1

Let $\mu=52,~\sigma=15,~n=25$

t-value for n - 1 = 24 degrees of freedom and 10% significance level is 1.318.

With given significance level population mean belongs to the interval $\mu\pm t\frac{\sigma}{\sqrt{n}}=52\pm1.318\frac{15}{\sqrt{24}}=52\pm4.04.$

The value of 50 fits into this interval, so we cannot infer that the population mean is not equal to 50.