Question

There are 6 Intro Statistics classes (say, groups) each with 15 students offered in the SP 2020 semester of a university. All the classes are taught by new graduate teaching assistants. The head of the department of Statistics wants to see if at least one class is significantly different from the overall instructional style. He decided to do an ANOVA F-test for the final marks. The ratio of variance between groups to variance within groups is 2.71. The P value of the test should be:

1. 0.0034
2. 0.1315
3. 0.0255

Answer 1

See this is an one way ANOVA. Here the effect of all 6 intro statistics courses are compared.

Here null hypothesis : all courses are equally effective

Alternative hypothesis: atleast one course is differently effective.

Let between group variance= sb and within group variance =sw and let the number of course be k=6 and total individuals studied=n =15*6=90.

Here test statistic is : Ft = $\frac{sb}{sw}*\frac{n-k}{k-1}$

Under null hypothesis, Ft~F_k-1,n-k

_{Here sb/sw=2.71, k=6,n=90}

So Ft ~ F_{​​​​​​5,84}

Observed Ft= 45.528

So p value is P(F_{​​​​​​5,84} > 45.528) = .0034 (using F table)

Answer 0.0034. that is option a is correct.

Hope the solution helps. Thank you.

(Please comment if you need further help)