Question

A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random and finds the mean number of runs scored is 7.4 with a sample standard deviation of 2.88.

Required:
Is it likely that his team's scores is different than the national average?

Answer 1

That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average

Explanation:

The National average number of runs scored by a LL team is

μ = 5.7

Sample Information:

size sample n = 5

sample average x = 7.4

sample standard deviation s = 2.88

Is required to investigate if that sample average is statistically different from the National average

We will do a test with 95 % of confidence Interval that means

significance level α = 5 % or α = 0.05.

The sample size is 5 then even when we assume normal distribution the sample size indicates that we need to use t-student distribution. Furthermore, as the question is if the sample average is different from the national the test will be a two-tail test.

Then α = 0.05 α/2 = 0.025

df = n - 1 df = 5 - 1 df = 4

Then from t-student table we get t(c) = 2.132

Hypothesis test:

Null Hypothesis H₀ x = μ

Alternative Hypothesis Hₐ x ≠ μ

To calculate t (s)

t(s) = ( x - μ ) / s/√n

t(s) = ( 7.4 - 5.7 )* 2.24 / 2.88

t(s) = 1.7* 2.24 / 2.88

t(s) = 1.32

Comparing t(s) and t(c)

1.32 < 2.132

That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average