Question

A professional baseball player claims he can get a hit 30% of the time based on batting average. During the next 10 games he had 38 at bats and only got 7 hits. Test the claim that the player gets a hit 30% of his at-bats with a significant level of 0.05

6. A professional baseball player claims he can get a hit 30% of the time based on his batting average However, during the next 10 games he had 38 at bats and only got 7 hits. Test the claim that the player gets a hit 30% of his at-bats with a 0.05 (8 Points - 2 Points for Error Question). Ho: H: Calculate test statistic: P-value: mp2 State your Conclusion: What would it mean if you made a TYPE II Error in the context of this scenario?

Answer 1

Ans:

$H_0:p=0.30$

$H_a:p\neq 0.30$

alpha=0.05

sample proportion=7/38=0.1842

Test statistic:

z=(0.1842-0.30)/sqrt(0.30*(1-0.30)/38)

z=-1.558

p-value=2*P(z<-1.558)=0.1193

As,p-value>0.05,we fail to reject the null hypothesis.

There is not sufficient evidence to reject the claim that the player gets a hit at 30% of his bats.

We will make type II error when we conclude that the player gets a hit at 30% of his bats,but in fact,he does not get a hit at 30% of his bat.

(as type II error is to fail to reject the null hypothesis,when null hypothesis is false)