The test statistic for this hypothesis test is the chi-square statistic (χ^2).
To calculate the chi-square statistic, we need to compare the observed frequencies (the number of students given each grade by the new lecturer) with the expected frequencies (the expected number of students given each grade according to the department's distribution of grades).
The expected frequencies can be calculated by multiplying the total number of students (80 in this case) by the corresponding proportions for each grade from the department's distribution (0.05 for A, 0.2 for B, 0.3 for C, 0.25 for D, and 0.2 for F).
Using these values, we can set up the following table:
Grade Observed Frequency Expected Frequency
A 12 (0.05) * 80 = 4
B 20 (0.2) * 80 = 16
C 26 (0.3) * 80 = 24
D 14 (0.25) * 80 = 20
F 8 (0.2) * 80 = 16
To calculate the chi-square statistic, we can use the formula:
χ^2 = Σ((Observed Frequency - Expected Frequency)^2 / Expected Frequency)
So, plugging in the observed and expected frequencies, we have:
χ^2 = (12-4)^2/4 + (20-16)^2/16 + (26-24)^2/24 + (14-20)^2/20 + (8-16)^2/16
Calculating this sum gives us the chi-square statistic, which we can then compare to the chi-square distribution with (number of categories - 1) degrees of freedom (in this case, 5-1 = 4) to determine whether there is sufficient evidence to suggest that the new lecturer's grading policy is different from that of the department.
The distribution of final grades given by a certain biometry department in the past was 5% A’s, 20% B’s, 30% C’s, 25% D’s and 20% F’s. A new lecturer gave the following number of students for the different grades:
Grade A B C D E
Number 12 20 26 14 8
You have to test whether there is sufficient evidence to suggest that the new lecturer’s grading policy is different from that of the department. The test statistic for this hypothesis test is
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