Let us denote the American League by subscript 1 and National League by subscript 2.
a). An independent two sample t-test would be appropriate for this situation.
b). The Hypothesis:
(Average number of runs is higher for American League)
Where are the population means of the American and National League.
c). The t-test statistic is 0.6022 and the p-value is 0.2759 for an one tailed test.
d). Since the p-value>0.05, we fail to reject the null hypothesis. Hence, we conclude that there is not enough evidence to claim that the average run scored by American League is more than the National League.
e)The 90% confidence interval is given by (-0.150,0.314).
f). We are 90% confident that the true population difference of the runs between American League and the National League is between -0.150 and 0.314.
g). Since this interval contains the value o, the confidence interval supports the conclusions in part(d)
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t-Test: Two-Sample Assuming Equal Variances | |||||
Amer | National | ||||
Mean | 4.519333333 | 4.437333333 | |||
Variance | 0.12486381 | 0.153220952 | |||
Observations | 15 | 15 | |||
Pooled Variance | 0.139042381 | s1 | 0.372884 | ||
Hypothesized Mean Difference | 0 | s2 | 0.365148 | ||
df | 28 | SE | 0.136158 | ||
t Stat | 0.602241787 | t | 1.701131 | ||
P(T<=t) one-tail | 0.275929758 | Limit | 0.231622 | ||
t Critical one-tail | 1.701130934 | diff | 0.082 | ||
P(T<=t) two-tail | 0.551859515 | Lower | -0.14962 | ||
t Critical two-tail | 2.048407142 | Upper | 0.313622 | ||
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