One of the old theories in major league baseball is that, in order to win a pennant a team has to win about seventy five ercent of its home games and bout fifty percent of its games away from home. After the first frew weeks of the season, the mudtown sloppers have eight wins and four losses at home, and six wins and five losses on the road. If we use the five percent level of significance, and we get a computed value to be +.59, can we conclude that the sloppers are more sloppy on the road than at home?
Is this one-tail or two tail
Let's denote the data for home games by subscript 1 and for away games by 2
Data given is as follows:
Sample sizes, n1 = 12, n2 = 11
Sample proportions for losses, p1 = 4/12 = 0.33, p2 = 5/11 = 0.45
Next we calculate standard error:
S = ((p1*(1-p1)/n1 + (p2*(1-p2)/n2)^0.5 = ((0.33*(1-0.33)/12 + (0.45*(1-0.45)/11)^0.5 = 0.168
Now we calculate the test statistic:
t = (p2-p1)/S = (0.45-0.33)/0.168 = 0.714
Degrees of freedom, df = n1 + n2 - 2 = 21
The corresponding p-value for this t-value is:
Given significance level, a = 0.05
Since this is a one tailed test, so we compare p with a.
Since p > a, so we cannot reject the null hypothesis, so we cannot say that sloppers are more sloppy in away games as compared to in home games.
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