A small appliance company is interesting in comparing delivery times of their product during two months. They wonder if the deliver times slow down in the summer since business slows down.

Question

The randomly select 6 orders from each month and track the delivery times. Here what they found:

May	54	49	68	66	62	62
August	50	65	74	64	68	72

Test if the delivery times in May are shorter than in August. Use the Wilcoxon ranked sum test with α = 0.05. A table has been provided below to help with work, if you want to use it.

Entry:?

Set:?

Rank:?

Answer 1

Null Hypothesis or H₀: May & August Delivery Times Are Equal.

Alternative Hypothesis or H₁: May Delivery Times Are Shorter Than August Delivery Times.

Organize the 2 sets of data into one table with Times in ascending order. The Month for each Time is shown and Rank numbers are given in ascending order. Equal Times are given "split" Rank numbers; 62 & 62 are given an equal Rank of 4.5 (the mean of 4 & 5, which would have been their Ranks for ascending Time value had they been unequal).

TIME---MONTH----------RANK

49---------May----------------1

50---------August------------2

54---------May----------------3

62---------May----------------4.5

62---------May----------------4.5

64---------August-------------6

65---------August-------------7

66---------May-----------------8

68---------May-----------------9.5

68---------August-------------9.5

72---------August------------11

74---------August------------12

Sample sizes are named here as n₁ (for May Times) equal to 6 and n₂ (for August Times) equal to 6.

Label the sum of the Rank Numbers for May Times as R since n₁ has been marked as the May sample size.

Then R = 1+3+4.5+4.5+8+9.5 or 30.5.

Enter a Table Of Lower & Upper Critical Values For The Wilcoxon Rank-Sum Test 

for a 1-Tailed Test with (α, n₁, n₂) = (0.05, 6, 6). The Table will return 28 & 50 as the critical values.

Here R at 30.5 falls just inside the range 28-to-50 so one "fails to reject" the null hypothesis H₀ and

concludes that the May & August delivery times are equal for all practical purposes at the 0.05 level of significance.