Question

Download data.online.xlsx. Online selling costs for products available online from top two US e-commerce retailers are to be analyzed. Use a 0.07 significance level to test the claim that Amazon has a lower selling price than Walmart. Include the hypothesis, test statistic, p-value, and conclusion.

Product	Category	Amazon	WalMart
Nespresso Pixie D60 Espresso Machine	Kitchen/Housewares	242.05	225.99
NatureMade Super B-Complex (460)	Grocery/Cosmetic	17.49	19.97
Crocs - Mens Classic	Clothing/Shoes	32.95	25.95
Altra Women's Superior 2 Trail	Clothing/Shoes	85.19	82.94
Tracfone 60MIN Card	Grocery/Cosmetic	24.95	19.99
Pero 7OZ	Grocery/Cosmetic	5.98	5.98
3-Way Gourmet Popcorn	Grocery/Cosmetic	49.99	31.27
Marmot Mens Zeus Jacket 2XL	Clothing/Shoes	120	126
Nectar in a Sieve	Miscellaneous	6.49	7.77
The Essential Yo-Yo Ma	Miscellaneous	13.98	14.75
DHP Emily Futon, Vanilla	Kitchen/Housewares	172.79	189
Huffy Nel Lusso Cruiser, Yellow	Miscellaneous	156.79	119
Celestial Tea, Assorted, 150 CT	Grocery/Cosmetic	28.52	27.98
Venus Swirl Razor, 2 Blade Refills	Grocery/Cosmetic	11.75	12.97
TI-30X IIS Scientific Calculator	Miscellaneous	12.95	12.95
Fitbit Blaze, Black	Miscellaneous	169	199.95
Pampers Easy Ups, 3T/4T, 148CT	Grocery/Cosmetic	41.25	43.51
Better Homes & Gardens 6-PC Towels	Kitchen/Housewares	27.62	15.49
Zoey Contemporary Display Shelf, Red	Kitchen/Housewares	320.17	437.98
Maglite LED Flashlight	Miscellaneous	25.47	38.99
Vera Wang Champagne Flutes	Kitchen/Housewares	124.99	125
Goodyear Wrangler Tire, 235/75R15 105S	Miscellaneous	74	126.99
Everest Fanny Waist Pack	Clothing/Shoes	5.9	9.99
Ravel Paris Bb Trumpet	Miscellaneous	381	419.28
Peanut M&Ms, 42OZ	Grocery/Cosmetic	8.54	8.98
KODAK PIXPRO FZ53 Compact Digital Camera	Miscellaneous	77	77
Gold's Gym Vinyl Weight Set, 100 lbs	Miscellaneous	72	60
Fruit of the Loom Mens No-Show Socks, 6 Pack	Clothing/Shoes	6.57	7.47
Speedo Vanquisher 2.0 Mirrored Swim Swimming Competition Goggle, Silver/Blue	Miscellaneous	18.02	17.65
Wilson Thrasher Racquetball Racquet	Miscellaneous	49.95	69.95

Answer 1

As the prices of Walmart and amazon do not follow Normal distribution, it would be wrong to apply it. Normality assumption is failed because qqnorm plot of both prices of Walmart and Amazon arenot straight lines.

Thus, we shall use non-parametric test (Wilcoxon Signed rank test)

If median of prices of Amazon is a and that of walmart is b. Our hypothesis is

wilcox.test(price ~ retail, data = y, paired = TRUE, alternative= "less")

Wilcoxon signed rank test with continuity correction

data: price by retail

V = 140, p-value = 0.122

alternative hypothesis: true location shift is less than 0