Question: The number of people attending a movie in three different theaters during the last one week is tabulated as shown. At α = 0.01, find the F test value and test the claim that the mean number of people attending the movie in each of the theaters are the same.
A ) 6.01, same B ) 6.05, different C ) 6.01, different D ) 6.05, same
Steps to derive
1 Let μ1, μ2, μ3 be the mean number of people attending the movie.
H0: μ1 = μ2 = μ3
H1: At least one mean is different from the others. [Null and alternative hypotheses.]
2k = 3 and N = 21, the degrees of freedom(d.f.) are d.f.N = k - 1 = 3 - 1 = 2 d.f.D = N - k = 21 - 3 = 18 and α = 0.01 The critical value from the F distribution table is 6.01 [k - number of groups N - sum of the sample sizes of the groups.]
3 The mean and variance of each sample are given below the table.
4 Grand mean X‾GM = ΣXN = 236+280+147+......+196+22021 = 446121= 212.4 [Substitute X values from the table.]
