Question

Listed below are amounts​ (in millions of​ dollars) collected from parking meters by a security company in a certain city. A larger data set was used to convict 5 members of the company of grand larceny. Find the mean and median for each of the two samples and then compare the two sets of results. Do the limited data listed here show evidence of stealing by the security​ company's employees?
Security companies:
Security Company (#'s on left) Other Companies (#'s on right)
1.6; 1.5
1.8; 2.1
1.6; 1.9
1.8; 2.2
1.7; 1.9
1.2; 1.7
1.1; 2.1
1.2; 2.2
1.2; 2.2
1.5; 1.8

Find the means.
The mean for the security company is $ ___ million and the mean for the other companies is $ ____?
Find the medians.
The median for the security company is $ ___ million and the median for the other companies is $ ____?
Compare the results. Choose the correct answer below.
A. The median is lower for the collections performed by other​companies, but the mean is lower for the security company.
B. The mean and the median for the security company are both lower than the mean and the median for the collections performed by other companies.
C. The mean and median appear to be roughly the same for all collections.
D. The mean and the median for the collections performed by other companies are both lower than the mean and the median for the security company.
E. The mean is lower for the security​ company, but the median is lower for the collections performed by other companies.


Do the limit data listed here show evidence of stealing by the security​ company's employees?
A. The sample size is not large enough to show any meaningful results.
B. Since the security company appears to have collected lower revenue than the other​ companies, there is some evidence of stealing by the security​ company's employees.
C. Since the security company does not appear to have collected lower revenue than the other​ companies, there is no evidence of stealing by the security​ company's employees.
D. Since the data is not​ matched, there is no evidence of stealing by the security​ company's employees.

Answer 1

Answer:

a i.) The mean for the security company is $ 1.47 million

a ii.) The median for the security company is $ 1.55 million

a iii.) The mean for the other companies is $ 1.96 million.

a iv.) The mean for the other companies is $ 2.0 million.

b) B. The mean and the median for the security company are both lower than the mean and the median for the collections performed by other companies.

c) B. Since the security company appears to have collected lower revenue than the other​ companies, there is some evidence of stealing by the security​ company's employees.

Step-by-step explanation:

By mean, we sum all the observation and divide by the sample size (n). Where sample size is the number of observations.

Mathematically,

$\bar{x} = \frac{\sum\limits_{i=1}^{n}{x_{i}}}{n}$, where xi is the observations or values given.

By median, we mean middle number. So, we sort the values in ascending or descending order and take the value(s) in the middle. If the sample size is even, we take the 2 middle values and obtain the average.

See below, R programming codes for the solution.

##########...... R code

s = c(1.6,1.8,1.6,1.8,1.7,1.2,1.1,1.2,1.2,1.5)

c = c(1.5,2.1,1.9,2.2,1.9,1.7,2.1,2.2,2.2,1.8)

length(s)

mean(s); median(s)

mean(c);median(c)

t = (mean(s)-mean(c))/sqrt((var(s) + var(c))/length(s))

pnorm(t)

##############################################

For question C, we compute the test statistics, and obtain the p-value, see the last two lines of the R codes.

And since the p-value is less than level of significance, the test is significant. Thus, we conclude that:

Since the security company appears to have collected lower revenue than the other​ companies, there is some evidence of stealing by the security​ company's employees.