Exhibit 11-1
In baseball, hits can be one of four types: singles, doubles, triples, or home runs. In the last baseball season, 64% of the hits were singles, 20% were doubles, 2% were triples, and 14% were home runs.
Spring training games are played in March before the regular season to help the players get in shape. A sports writer thinks that perhaps the distribution of types of hits is different in these games. The sportswriter gathers a random sample of 251 hits from spring training games. Here is the distribution of types of hits for these games:
-Refer to Exhibit 11-1. At the .05 level of significance, test the hypothesis that the proportions of the different types of hits in the spring is the same as for last year's season.

Question

Exhibit 11-1
In baseball, hits can be one of four types: singles, doubles, triples, or home runs. In the last baseball season, 64% of the hits were singles, 20% were doubles, 2% were triples, and 14% were home runs.
Spring training games are played in March before the regular season to help the players get in shape. A sports writer thinks that perhaps the distribution of types of hits is different in these games. The sportswriter gathers a random sample of 251 hits from spring training games. Here is the distribution of types of hits for these games: 
-Refer to Exhibit 11-1. At the .05 level of significance, test the hypothesis that the proportions of the different types of hits in the spring is the same as for last year's season.

Quizplus · Accepted Answer

The Answer is 1)p₁ = the true proportion of spring training hits that are singles
p₂ = the true proportion of spring training hits that are doubles
p₃ = the true proportion of spring training hits that are triples
p₄ = the true proportion of spring training hits that are home runs
2)H₀ : p₁ = .64, p₂ = .20, p₃ = .02, p₄ = .14
3)H_a : H₀ isn't true
4)α = .05
5)

1)p<sub>1</sub> = the true proportion of spring training hits that are singles p<sub>2</sub> = the true proportion of spring training hits that are doubles p<sub>3</sub> = the true proportion of spring training hits that are triples p<sub>4</sub> = the true proportion of spring training hits that are home runs 2)H<sub>0</sub> : p<sub>1</sub> = .64, p<sub>2</sub> = .20, p<sub>3</sub> = .02, p<sub>4</sub> = .14 3)H<sub>a</sub> : H<sub>0</sub> isn't true 4)α = .05 5) 7)X<sup>2</sup> = 1.94 df = 3 8)P-value = P(X<sup>2</sup> > 1.94) > .100 9)Since the P-value > α, we fail to reject H<sub>0</sub>. We cannot conclude that the proportions of different types of hits in spring training is different than last year's season.

7)X² = 1.94 df = 3
8)P-value = P(X² > 1.94) > .100
9)Since the P-value > α, we fail to reject H₀. We cannot conclude that the proportions of different types of hits in spring training is different than last year's season.

Exhibit 11-1 In Baseball, Hits Can Be One of Four Types: Singles