Test the hypothesis that the average price of diamonds in the available data is larger than $4500 after filtering out the cheapest diamonds (< $1000)
Single mean test
Data : diamonds
Filter : price > 1000
Variable : price
Null hyp.: the mean of price = 4500
Alt. hyp.: the mean of price is > 4500
mean t.value p.value df 2.5% 97.5% sd n
5104.718 7.016 < .001 2183 4962.883 Inf 4028.095 2184
Compare diamond prices by the quality of the 'cut'. It seems that diamonds with an ideal cut cost less than than diamonds with a premium cut. Seems strange. Perhaps we should use regression to control for the carats of the diamond. Try it!
Pairwise comparisons (no adjustment)
Data : diamonds
Filter : price > 1000
Variables: cut, price
Samples : independent
mean n sd se ci
Fair 4701.771 96 3742.952 382.013 758.393
Good 5141.244 213 3663.915 251.047 494.869
Very Good 5206.187 492 3897.686 175.721 345.258
Premium 5469.652 592 4261.311 175.139 343.970
Ideal 4807.550 791 4038.235 143.583 281.850
Alt. hyp. Null hyp. diff p.value
Fair not equal to Good Fair = Good -439.473 0.338
Fair not equal to Very Good Fair = Very Good -504.416 0.232
Fair not equal to Premium Fair = Premium -767.881 0.07
Fair not equal to Ideal Fair = Ideal -105.779 0.796
Good not equal to Very Good Good = Very Good -64.943 0.832
Good not equal to Premium Good = Premium -328.408 0.284
Good not equal to Ideal Good = Ideal 333.694 0.249
Very Good not equal to Premium Very Good = Premium -263.465 0.288
Very Good not equal to Ideal Very Good = Ideal 398.637 0.079
Premium not equal to Ideal Premium = Ideal 662.102 0.004
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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Visualize the relationship between diamond prices, carats, and the cut of the diamond.
