Question

A men's softball league is experimenting with a yellow baseball that is easier to see during night games. One way to judge the effectiveness is to count the number of errors. In a preliminary experiment, the yellow baseball was used in 10 games and the traditional white baseball was used in another 10 games. The number of errors in each game was recorded and is listed here. Can we infer that there are fewer errors on average when the yellow ball is used?

Yellow 5 2 6 7 2 5 3 8 4 9

White 7 6 8 5 9 11 8 3 6 10

Answer 1

There cannot be equal errors in both and yellow has fewer errors.

Explanation:

we can do paired t test for these two colours

`H_0: \bar = \bar y\\H_a: \bar <  \bar y\\`

(one tailed test)

df = 9

The data can be tabulated as follows:

Yellow white

5 7

2 6

6 8

7 5

2 9

5 11

3 8

8 3

4 6

9 10

t-Test: Paired Two Sample for Means

Yellow white

Mean 5.1 7.3

Variance 5.877777778 5.788888889

Observations 10 10

Pearson Correlation -0.139051655

Hypothesized Mean Difference 0

df 9

t Stat -1.908439275

P(T<=t) one-tail 0.044341411

t Critical one-tail 1.833112923

P(T<=t) two-tail 0.088682822

t Critical two-tail 2.262157158

Since p value one tailed = 0.0443 and it is <0.05 our significance level, we reject null hypothesis.

There cannot be equal errors in both and yellow has fewer errors.