Question

Acme Toy Company prints baseball cards. The company claims that 30% of the cards are rookies, 60% are veterans, and 10% are All-Stars. Suppose a random sample has the following cards. Test Acme's claim that the distribution is a good fit with the prints of baseball cards at an α=0.05α=0.05 level of significance.

Category Observed
Frequency Expected
Frequency
Rookies 25 ??????
Veterans 110 ??????
All-Stars 15 ??????

Complete the table by calculating the expected frequencies.

Answer 1

The expected frequencies for the baseball cards categories based on Acme Toy Company's claims are 45 for Rookies, 90 for Veterans, and 15 for All-Stars. These are calculated by applying the claimed percentages to the total number of observed cards, which is 150.

Step-by-step explanation:

The student is tasked with verifying the claims of Acme Toy Company about the distribution of their baseball cards categories using a chi-square goodness of fit test. To do this, we calculate the expected frequencies based on the total number of observed cards and the company's claimed percentages.

Let's define the observed total cards as O, which is the sum of observed frequencies: O = 25 (Rookies) + 110 (Veterans) + 15 (All-Stars) = 150 cards.

Now, we calculate the expected frequencies based on the percentages provided:

• Rookies: 30% of 150 = 0.30 × 150 = 45 cards
• Veterans: 60% of 150 = 0.60 × 150 = 90 cards
• All-Stars: 10% of 150 = 0.10 × 150 = 15 cards

With the expected frequencies calculated, the student can proceed to perform the chi-square test using the observed and expected frequencies to determine if the company's claims are statistically valid at an α = 0.05 level of significance.