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 they are currently using.

Seven cashiers are randomly selected, and the number of grocery items they can process in three minutes is measured for both the old cash register and the new cash register. The results of the test are as follows:

Cashier	Old Cash Register	Old Cash Register
1	60	65
2	70	71
3	55	55
4	72	75
5	62	65
6	52	58
7	58	57

Using a 5% level of significance, can we conclude that the new cash register will allow cashiers to process a significantly larger numbers on average than the old cash register? Do steps 0 –5.

0.

1.

2.

3.

4.

5.

Answer 1

Here we have paired data so paired t test will be used. Let d = old cash register - new cash register

Following table shows the calculations:

Old	New	d	(d-mean)^2
60	65	-5	6.6049
70	71	-1	2.0449
55	55	0	5.9049
72	75	-3	0.3249
62	65	-3	0.3249
52	58	-6	12.7449
58	57	1	11.7649
Total		-17	39.7143

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Conclusion: There is evidence to conclude that the new cash register will allow cashiers to process a significantly larger numbers on average than the old cash register.