Question

The grades in a statistics course for a particular semester were as follows:

x=A B C D F F G H

f= 136 60 34 12 29 1 3 1

Test the hypothesis at the 0.05 level of significance does thr distribution of grades follow poison distribution

Answer 1

Given the grades in a statistics course for a particular semester.

To test: whether grades follow grades follow Poisson distribution at 0.05 level of significance.

The hypotheses to be tested are:

H₀: The data is from Poisson distribution

H₁: The data is not from Poisson distribution

We estimate parameter of Poisson distribution as

$λ= \frac{\sum fx}{\sum f} \\ λ=2.0809$

The Chi square test is given by

$χ^2 = \sum \frac{(f-e)^2}{e} \sim χ^2_{n-2, α}$

where the test statistic is calculated as follows:

The critical value of Chi square test is

$χ^2_{n-2, α} = χ^2_{6, 0.05} = 12.592$

Since Chi square calculated value greater than Chi square critical value, we reject the null hypothesis and can conclude that data is not from Poisson distribution.