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 companys employees? security company: 1.5 1.1 1.5 1.1 1.4 1.3 1.7 1.3 1.3 1.2 other companies: 1.6 1.9 2.3 1.8 2.3 1.7 1.9 1.8 1.8 2.2 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 is lower for the security company, but the median is lower for the collections performed by other companies. 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 and median appear to be roughly the same for all collections. do the limited data listed here show evidence of stealing by the security companys employees? a. the sample size is not large enough to show any meaningful results. b. since the data is not matched, there is no evidence of stealing by the security companys employees. c. since the security company appears to have collected lower revenue than the other companies, there is some evidence of stealing by the security companys employees. d. 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 companys employees.

Explanation:

Step1: Calculate mean of security company data

The sum of security company amounts \(15 + 11+1.5 + 11+1.4+13+17+13+13+12 = 110.9\). There are \(n = 10\) data - points. The mean \(\bar{x}_1=\frac{110.9}{10}=11.09\).

Step2: Arrange security company data in ascending order

\(1.4,1.5,11,11,12,13,13,13,15,17\). Since \(n = 10\) (even), the median \(M_1=\frac{12 + 13}{2}=12.5\).

Step3: Calculate mean of other companies data

The sum of other companies amounts \(16+19+23+18+23+17+19+18+18+22 = 193\). There are \(n = 10\) data - points. The mean \(\bar{x}_2=\frac{193}{10}=19.3\).

Step4: Arrange other companies data in ascending order

\(16,17,18,18,18,19,19,22,23,23\). Since \(n = 10\) (even), the median \(M_2=\frac{18 + 19}{2}=18.5\).

Step5: Compare mean and median

We have \(\bar{x}_1 = 11.09\), \(M_1 = 12.5\), \(\bar{x}_2=19.3\), \(M_2 = 18.5\). 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.

Step6: Analyze evidence of stealing

Since the security company appears to have collected lower revenue (both in terms of mean and median) than the other companies, there is some evidence of stealing by the security company's employees.

Answer:

The correct answer for the comparison of results is 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.
The correct answer for evidence of stealing is C. 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.