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	30	?
Veterans	100	?
All-Stars	20	?

1. Complete the table by calculating the expected frequencies.
   
2. What is the chi-square test statistic? Round to three decimal places.
   χ2=
   
3. What are the degrees of freedom?
   degrees of freedom =
   
4. What is the pp-value for this sample? Round to four decimal places.
   p value =

Answer 1

Data	Observed values (fo)	Expected Proportions	Expected values (fe)	(fo-fe)2/ fe
Rookies	30	0.300	45.00	5.000
veterans	100	0.600	90.00	1.111
all stars	20	0.100	15.00	1.667
Total	150	1.000	150.00	7.778

= 7.778

critical = 5.991

Degree of freedom = 3-1 = 2

p value = 0.0205

As p value (0.0205) is less than α=0.05, we reject the Null hypothesis.

Also ( 7.778) is greater than critical, we reject the Null hypothesis.