A random sample of 51scores is collected with a sample mean of 75 and a sample variance of 10. Test the following hypotheses at the .05 level of significance:

$\begin{array}{l}H_{0}: \sigma^{2}=7 \\H_{1}: \sigma^{2} \neq 7\end{array}$

Question

A random sample of 51scores is collected with a sample mean of 75 and a sample variance of 10. Test the following hypotheses at the .05 level of significance:

\begin{array}{l}H_{0}: \sigma^{2}=7 \\H_{1}: \sigma^{2} \neq 7\end{array}

Quizplus · Accepted Answer

The Answer is Degrees of freedom (_v) are equal to _n_-_{1, thus 5}_{1 - 1}_{= 5}_{0.
The hypothesized populati}_{on variance is provided to us (7}_{).
Plugging these values into the formula, we find the test statistic value:}

\chi^{2}=\frac{v s^{2}}{\sigma_{0}^{2}}=\frac{50(10)}{7}=71.429

_{From Appendix Table 3, and using an alpha level of .05}_{(i.e., tabled values listed under .975 and .025)}_{and degrees of freedom (}_v_{) of}₅_{0, we determine the critical values to be}_71.4202_and_32.3574_{. As t}_{he test statistic (71.429}₎_does_{exceeds one of the critic}_{al values by falling into the upper-tail critical region (71.429 >}_71.4202_{), our decision is to reject the null hypothesis.}

A Random Sample of 51scores Is Collected with a Sample H0:σ2=7H1:σ2≠7\begin{array}{l}H_{0}: \sigma^{2}=7 \\H_{1}: \sigma^{2} \neq 7\end{array}H0​:σ2=7H1​:σ2=7​

A Random Sample of 51scores Is Collected with a Sample $\begin{array}{l}H_{0}: \sigma^{2}=7 \\H_{1}: \sigma^{2} \neq 7\end{array}$