Answer to Question #182400 in Statistics and Probability for najie

Question

A sample size 40 from a non-normal population yielded the sample mean X= 71 and S² =200. Test H₀: µ=72 against H1: µ≠72. Use α= 0.05.

Answer 1

Since the sample is large enough(n>30), the sampling distribution of the mean is normal.

we calculate the test statistic,

$t=\frac{\bar X-\mu}{\frac{s}{\sqrt n}}$

$=\frac{71-72}{\frac {\sqrt{200}}{\sqrt{40}}}$

=-0.447

The degrees of freedom is (n-1)=40-1=39. This is a two sided hypothesis, the critical value will be

$t_{{\alpha/2}, 39}=t_{0.025,39}=2.023$ from the t-tables.

if the absolute t- value is greater than the critical value we reject the null hypothesis.

|-0.447|<2.023

we therefore fail to reject the null hypothesis at 5% level of significance. The population mean is equal to 72.