Question

The management for a large grocery store chain would like to determine if a new cash register will enable cashiers to process a larger number of items on average than the cash register which they are currently using. Nine cashiers are randomly selected, and the number of grocery items which they can process in three minutes is measured for both the old cash register and the new cash register.

Without making any assumptions about the distribution, do the data provide conclusive evidence that the new cash register enables cashiers to process a significantly larger number of items than the old cash register? Use the Wilcoxon signed-rank test to analyze the results.

Number of Grocery Items Processed in Three Minutes

Cashier	11	22	33	44	55	66	77	88	99
Old Cash Register	6464	6666	5858	6666	6262	5757	6060	6767	7878
New Cash Register	6363	7373	6464	6868	5858	6565	6262	7777	7373

Step 1 of 2:

Find the value of the test statistic to test if the new cash register enables cashiers to process a significantly larger number of items than the old cash register. Round your answer to two decimal places, if necessary.

Step 2 of 2:

Make the decision to reject or fail to reject the null hypothesis that the number of items that the new cash register enables cashiers to process is less than or equal to the number of items that the old cash register enables cashiers to process, and state the conclusion in terms of the original problem. Use α=0.01α=0.01.

Answer 1

Step 1 of 2:

-1.48

Step 2 of 2:

The p-value from the output is 0.0693.

Since the p-value (0.0693) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Therefore, we cannot support the claim that the new cash register enables cashiers to process a significantly larger number of items than the old cash register.

	variables:	Old Cash Register - New Cash Register
	10	sum of positive ranks
	35	sum of negative ranks
	9	n
	22.500	expected value
	8.441	standard deviation
	-1.48	z
	.0693	p-value (one-tailed, lower)
No.	Data	Rank
1	101	1
2	-707	7
3	-606	6
4	-202	2.5
5	404	4
6	-808	8
7	-202	2.5
8	-1010	9
9	505	5