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Given that randomly selected community college students, 43 used a computer, 102 used a calculator with built-in statistics functions, and 65 used a table from the textbook.

Of some randomly selected university students, 28 used a computer, 33 used a calculator with built-in statistics functions, and 40 used a table from a textbook.

The null hypothesis is shown below: $H_0$: The distribution of college statistics students is same as the distribution of university statistics students.

Against the alternative hypothesis as shown below:

$H_a:$The distribution of college statistics students is different from the distribution of university statistics students.

The degrees of freedom can be calculated by the formula given below:

$df=(numberofcolumn-1)$

Therefore

$df=3-1$

=2

$df=3-1$

From above calculation, it is clear that the distribution for the test is ${\mathrm{χ}}_2^2$.

The observed value table is already given in the textbook. Calculate the expected frequencies by using the formula given below:

$E=\frac{\left(\text{row total}\right)\left(\text{column total}\right)}{\text{overall total}}$

All calculations can be done in excel worksheet. Hence, the expected localid="1649136146590" $\left(E\right)$values table is shown below:

The test statistic of the independence test is given below

$\text{Test statistic}=\underset{(i×f)}{∑}\frac{(O-E{)}^2}{E}$

To calculate $\frac{(O-E{)}^2}{E}$apply the formula

$=\left((B4-B11{)}^2\right)/B11$

same formula up to cell D19. After that, take the total of columns total and rows total. The table of the test statistics is shown below:

The $p$-value can be calculated in excel by using CHIDIST ( ) formula as shown below:

Hence the p-value is 0..29

The Chi-square sketch is given below

i. Alpha:$0.05$

ii: Decision: Reject the null hypothesis$H_0$

iii. Reason for decision: Because$p$-value $<\mathrm{Î\pm }$

iv. Conclusion: There is sufficient evidence to insure that the distribution of college statistics students is different from the distribution of university statistics students.