Question

A. Listed below are the amounts (in millions of dollars) collected from parking meters by a security company in your city in the previous 18 months, alongside the average amounts from another company. These data were used to convict 5 members of the security company in your city of grand larceny.

1. Do the limited data listed here show evidence of stealing by the security​ company's employees – why or why not?

Month:	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
Security Company	1.1	1.1	1.3	1.3	1.1	1.1	1.7	1.7	1.2	1.2	1.6	1.6	1.2	1.2	1.2	1.2	1.5	1.5
Other Company	1.6	1.6	2.3	2.3	2.2	2.2	1.5	1.5	2.2	2.2	2.1	2.1	2.3	2.3	1.5	1.5	1.5	1.5

Answer 1

Here, though the security staffs or the company is altogether different,the data is paired data, since, the amounts collected corrospond to same month.
Here, we are to test:

where,




We form the following table for the benefit of our calculation:

Month	Other Company	Security Company	d
1	1.6	1.1	0.5
2	1.6	1.1	0.5
3	2.3	1.3	1
4	2.3	1.3	1
5	2.2	1.1	1.1
6	2.2	1.1	1.1
7	1.5	1.7	-0.2
8	1.5	1.7	-0.2
9	2.2	1.2	1
10	2.2	1.2	1
11	2.1	1.6	0.5
12	2.1	1.6	0.5
13	2.3	1.2	1.1
14	2.3	1.2	1.1
15	1.5	1.2	0.3
16	1.5	1.2	0.3
17	1.5	1.5	0
18	1.5	1.5	0

Since, population standard deviation is not known, we use the test statistic

where,



Hence,


Under ,


We reject at 5% level of significance iff

Now,


We observe that,


Hence, we reject at 5% level of significance and conclude that, the average amount collected by other company is lesser than that collected by the security company and hence, there is an evidence of stealing.