Question

The data in ‘Problem 4’ show the top 30 home run totals in each League in Major League Baseball in 2018. Use Excel to perform the appropriate test to see if the American League’s top home run hitters had a higher average number of home runs than the top National League home run hitters did. Assume both data sets come from normally distributed populations.

one tailed or two:

Test statistic:

p-value:

decision:
Did AL Average more HR than NL Did:

American	National
League	League
48	38
43	37
40	36
39	36
39	35
38	35
38	34
37	34
32	34
32	34
31	33
30	32
30	30
29	29
27	28
27	26
27	26
27	26
27	25
27	25
27	25
26	24
25	24
25	24
25	24
24	23
24	23
24	23
24	23
24	23

Answer 1

Here we are going to use two sample t test because sample size is not >30. Assuming equal variance because there is no large difference in standard deviation.

In excel -> data -> data analysis -> two sample t test (assuming equal variance) -> select column and get the output below.

We use excel to test the American League’s top home run hitters had a higher average number of home runs than the top National League home run hitters did.

H₀ : µ₁ = µ₂

H₁ : µ₁ > µ₂

_{This is one tailed test} because in alternative hypothesis > show one tailed test.

t-Test: Two-Sample Assuming Equal Variances
	Variable 1	Variable 2
Mean	30.53333	28.96667
Variance	43.70575	27.48161
Observations	30	30
Pooled Variance	35.59368
Hypothesized Mean Difference	0
df	58
t Stat	1.017035
P(T<=t) one-tail	0.15668
t Critical one-tail	1.671553
P(T<=t) two-tail	0.313361
t Critical two-tail	2.001717

Test statistics: 1.017

P value for one tailed = 0.1567

Decision : Since P value = 0.1567 > 0.05 so we failed to reject null hypothesis.

Conclusion: There is no strong evidence to claim that American League’s top home run hitters had a higher average number of home runs than the top National League home run hitters did at 5% level of significance.