Question

Acme Toy Company sells baseball cards in packages of 100. Three types of players are represented in each package -- rookies, veterans, and All-Stars. The company claims that 30% of the cards are rookies, 60% are veterans, and 10% are All-Stars. Cards from each group are randomly assigned to packages.

Suppose you bought a package of cards and counted the players from each group. What method would you use to test Acme's claim that 30% of the production run are rookies; 60%, veterans; and 10%, All-Stars. Explain your choice.

Answer 1

As we are testing the claim here whether 0% of the production run are rookies; 60%, veterans; and 10%, we are testing the distribution of the given variable here, which is a goodness of fit test here. This is therefore a chi square test for which the chi square test statistic is computed as:

Where O_i would be the observed frequencies obtained from the package of 100 selected.

The expected frequencies E_i for each of the 3 categories is computed as:
= Total Frequency * Proportion of the respective category in the null hypothesis that are 30%, 60% and 10% respectively.

The degrees of freedom here is given as: n - 1 = 2

After computing this we compute the p-value from the chi square distribution tables for 2 degrees of freedom.