a teacher figures that final grades in the statistics 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. find only the test statistics to test the claim that the grade distribution for the department is different than expected. be sure to set up the equation. do not conduct the hypothesis testing. grade a b c d f number 42 36 60 8 14

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KarpaT KarpaT · Answer 1 · 2022-12-17T12:19:23+01:00

5.25 option c is the test statistics for the given data.

Given,

The observed values;-

A: 36

B: 42

C: 60

D: 14

E: 8

Total =160

To verify the following claim, a chi square test must be performed:

H0: The proportions for the final grades are the same.

H1: The final grade proportions varies from one another.

The level of significance assumed for this case is α = 0.01

The statistic to check the hypothesis is given by:

X² = ∑ⁿi = 1 (Oi - Ei)²/Ei

Now all that remains is to use the following formula to determine the predicted values, Ei = % × total

And the calculations are given by:

EA = 0.25 × 160 = 40

EB = 0.25 × 160 = 40

EC = 0.4 × 160 = 64

ED = 0.05 × 160 = 8

EF = 0.05 × 160 = 8

Here, the statistics;-

X² = (36 - 40)²/40 + (42 - 40)²/40 + (60 - 64)²/64 + (14 - 8)²/8 + (8 -8)²/8

= 16/40 + 4/40 + 16/64 + 36/8 + 0/8

= 5.25

Therefore,

The test statistics for the given data is option c 5.25

Learn more about test statistics here;

https://brainly.com/question/16768155

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