A teacher figures that final grades in the chemistry department are distributed as: A, 25%; B, 25%;C, 40%;D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic x^2 to determine if the grade distribution for the department is different than expected. Use α = 0.01. Grade A B C D F
Number 36 42 60 14 8

a. 6.87
b. 0.6375
c. 5.25
d. 4.82

And now we can calculate the statistic:  

The answer would be:

c. 5.25

Step-by-step explanation:

The observed values are given by:

A: 36

B: 42

C: 60

D: 14

E: 8

Total =160

We need to conduct a chi square test in order to check the following hypothesis:  

H0: There is no difference in the proportions for the final grades

H1: There is a difference in the proportions for the final grades

The level of significance assumed for this case is  

The statistic to check the hypothesis is given by:  

Now we just need to calculate the expected values with the following formula  

And the calculations are given by:  

And now we can calculate the statistic:  

The answer would be:

c. 5.25

Now we can calculate the degrees of freedom for the statistic given by:  

And we can calculate the p value given by:  

The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis

0.02040816326