Was the price of silver in 2007 significantly different than it was in 2008?
Side by side, we have two lists of prices of silver, the highest price in a given month in 2007, followed by the highest price in that same month in 2008. Take the differences in the prices and find the average and standard deviation. The size of the list is 12, so the degrees of freedom are 11. If we assume we did not know which year showed higher prices when we started this experiment, it make sense to make this a two-tailed test. Just for a change of pace, let us use the 90% confidence level.
Mo.___2007___2008
Jan.__13.45__16.23
Feb.__14.49__19.81
Mar.__13.34__20.67
Apr.__14.01__17.74
May___12.90__18.19
Jun.__13.19__17.50
Jul.__12.86__18.84
Aug.__12.02__15.27
Sep.__12.77__12.62
Oct.__14.17__11.16
Nov.__14.69__10.26
Dec.__14.76__10.66
Find the test statistic t, the threshold from Table A-3 and determine if we should reject H0, which in matched pairs tests is always that mu1 = mu2.
Answers in the comments.
1 comment:
Here are the differences,
Mo.___2007___2008
Jan.__13.45__16.23 -2.78
Feb.__14.49__19.81 -5.32
Mar.__13.34__20.67 -7.33
Apr.__14.01__17.74 -3.73
May___12.90__18.19 -5.29
Jun.__13.19__17.50 -4.31
Jul.__12.86__18.84 -5.98
Aug.__12.02__15.27 -3.25
Sep.__12.77__12.62 +0.15
Oct.__14.17__11.16 +3.01
Nov.__14.69__10.26 +4.43
Dec.__14.76__10.66 +4.10
d-bar = -2.19
s_d = 4.09
When Area in Two tails = .10 and d.f. = 11, our threshold is 1.796, and since it's two tailed, we have both -1.796 and +1.796.
t = -2.19/4.09*sqrt(12) = -1.855
(If you don't round the answers first, it's -1.854.)
In either case, we are below the low threshold for 90% confidence, so we reject the null hypothesis that the values were the same.
Post a Comment