Question

A sample of 14 items provides a sample standard deviation of 3.8. Test the following hypotheses using a = 0.05. What is your conclusion? Use both the p-value approach and the critical value approach. Ho : o2 < 30 Hq : 02 > 30 Test statistic = (to 2 decimals) p-value low from table = (to 3 decimals). Use Table 11.1. p-value high from table = (to 3 decimals). Use Table 11.1. Xổ.05 = (to 3 decimals) Reject Ho if x² > (to 3 decimals) ( - Select your answer -

Answer 1

Test Statistics:

Test Statistics

The Chi-Squared statistic is computed as follows:

$\chi^2 = \frac{(n-1) s^2}{\sigma^2} = \frac{(14-1)\cdot 14.44}{ 30} = 6.257$

p-value low from the table = 0.025

p-value high from the table = 0.975

$\chi^2_{0.05}$ = 22.362

Reject Ho if $\chi^2_{0.05}$ > 22.362

Here, $\chi^2$ < $\chi^2_{0.05}$ ( therefore we failed to reject the null hypothesis )