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Econ 2310 Business Statistics: Problem Set #1 Instructions: You may use Excel and/or a calculator to...

Econ 2310

Business Statistics: Problem Set #1

Instructions: You may use Excel and/or a calculator to complete this assignment. Please show work or reference what Excel commands you used to solve the problems.

  1. You are given the following two series on income and credit scores.

Income

FICO

39

625

27

600

57

710

31

595

34

610

50

840

38

726

62

710

43

635

49

560
  1. Find the covariance and the correlation coefficient. (B) Do credit scores increase, decrease, stay the same, with Income? (C) Create a scatter plot with Income and credit score. What do you see?
  1. Suppose you flip a fair coin four time. (A) What is the probability you will get all four heads? (B) All four tails? (C) Either all four heads or four tails? (D) Anything but four heads or four tails?

  1. Crime and Punishment: In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.    
  1. If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.
  2. If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison.

  1. In the BS Lottery (which stands for “Business Statistics”, of course), players choose 5 numbers out of 30. They win if they choose the same 5 numbers as our machine, which selects the numbers randomly. (A) How many permutations are possible? (B) How many combinations are possible?

  1. Below is a table of X and its frequency. What is the mean of X? What is the standard deviation of X? What is the variance of X?

X

Frequency

2

20%

5

10%

8

15%

10

30%

12

25%

Solutions

Expert Solution

A. Find the covariance and the correlation coefficient.

X Y* X*Y X^2 Y^2
39 625 24375 1521 390625
27 600 16200 729 360000
57 710 40470 3249 504100
31 595 18445 961 354025
34 610 20740 1156 372100
50 840 42000 2500 705600
38 726 27588 1444 527076
62 710 44020 3844 504100
43 635 27305 1849 403225
49 560 27440 2401 313600
Sum = 430 6611 288583 19654 4434451

Credit Score increases with income.

milcah answered 2 years ago
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