Answer
$H_0$ : The proportions of the eighth-graders were asked about the frequency with which they used calculators while taking tests or quizzes are as follow: 28% never, sometimes 51% and always 21%.
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.05, and the degrees of freedom are 3-1=2 , the critical value is 5.991.
Step 3:
Expected Value:
0.28 * 140 = 39.2
0.51 * 140 = 71.4
0.21 * 140 =29.4
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(30-39.2)^{2}}{39.2}$ + $\frac{(78-71.4)^{2}}{71.4}$ + $\frac{(32-29.4)^{2}}{29.4}$
=2.159+0.61+0.23
=2.999
Step 4:
Since 2.999 < 5.991, the decision is not to reject the null hypothesis.
Step 5:
There is no enough evidence to reject the claim and hence we conclude that the proportions do not differ from the national report.
