You own a small tea company, Sweet Leaf, NASDQ ticker symbol LEAF. You are looking at marketing costs versus benefits. Your production manager says it doesn't matter which tea you produce, all tea is the same. You say otherwise. You hire a consumer research firm headed my Matt Stat. He randomly interviews 100 consumers of your tea and the results are listed below.
BRAND PREFERRED NUMBER
Mumbo Jumbo 16
Purple Passion 27
British Experience 18
China Drift 17
The competing sides are a uniform distribution like the production manager says, or what your customers say. Run a goodness of fitness test to see if the distribution is uniform, or if the brands are different.
We use chi-squared test. The hypotheses are
H0: the distribution is uniform;
Ha: the distribution is NOT uniform.
Now we can compute the test statistic
The solution examines the goodness of fitness with statistics.