A company that provides cybersecurity services to small and medium-sized businesses, SafeOcean, offers several types of services. Most client businesses start by paying for basic protection services, but many seem to shift to more complex products as they gain confidence in SafeOcean. The price of the monthly subscription depends on the services provided, size of the client company and negotiations between the two parties. SafeOcean is trying to determine whether clients really do subscribe to more complex and expensive products with time. The table below lists, for a sample of current SafeOcean clients, the price of monthly subscription and for how many months they have been SafeOcean's customers.

Considering the variable Price only, answer the following questions:
a) Use the sample prices to estimate the mean and the standard deviation of the variable Price. (5%)
b) SafeOcean classifies all observations that are two standard deviations above or below the mean as outliers. Considering the variable Price only, how many outliers are there in this sample dataset? Justify. (10%)
c) Knowing that the variable Price follows a normal distribution, determine the price value that is surpassed 90% of the times (the price that is lower than 90% of the distribution). (10%)

Considering the sample values of both variables, Price and Duration (of the connection between client and SafeOcean), answer the following questions:
d) Compute the covariance and correlation between the variables Price and Duration. (5%)
e) Represent the relationship between the variables Price and Duration using a scatter plot. (10%)
f) How would you classify or describe the relationship between the two variables? Justify. (5%)

 

Question 2B Client ID 1805 6779 8092 4113 8900 1653 3816 1379 1143 5456 5582 8397 9336 7397 1714 5736 2808 6413 9680 5114 7033 5465 5842 6027 4713 7646 4306 2143 4224 6568 5732 5994 7928 2941 1512 Price ($) 889.62 593.63 1177.16 953.87 813.11 618.86 1054.75 1220.73 1016.13 1411.02 1213.71 917.84 733.82 501.35 934.01 707.58 882.46 1731.17 994.99 651.01 739.69 1045.03 927.66 1196.33 650.23 980.13 442.75 734.05 1143.47 227.54 728.82 1067.55 1296.32 471.19 702.71 Duration (months) 38 37 44 47 29 41 39 60 48 54 41 32 26 34 47 39 47 32 52 31 26 48 51 54 58 42 7 40 39 10 42 48 60 22 41