Statistics Case Study 1

Statistics

Case Study-1

Age Weeks Employed

55 21

30 18

23 11

52 36

41 19

25 12

42 7

45 25

25 6

40 21

25 13

25 11

59 34

49 27

33 18

35 20

a.

Age Weeks Employed

Mean 37.75 Mean 18.6875

Standard Error 2.974195 Standard Error 2.188452

Median 37.5 Median 18.5

Mode 25 Mode 21

Standard Deviation 11.89678 Standard Deviation 8.753809

Sample Variance 141.5333 Sample Variance 76.62917

Kurtosis -1.17143 Kurtosis -0.21626

Skewness 0.337402 Skewness 0.522601

Range 36 Range 30

Minimum 23 Minimum 6

Maximum 59 Maximum 36

Sum 604 Sum 299

Count 16 Count 16

Confidence Level(99.0%) 8.764138 Confidence Level(99.0%) 6.44877

b. 99% confidence interval estimate for mean age of newly hired employees;

37.75 Ð'ÐŽV 8.76 = 28.99

to

37.75 + 8.76 = 46.51

c. Hypothesis:

Decision Rule: Reject Ho if t > t-critical

Do not reject Ho if t < t-critical

t-critical = t0.01,15 =2.602

0.771 < 2.602

Therefore, at a 99% Confidence Level the Null Hypothesis can not be rejected and we can not state that RiversideÐ'ÐŽÐ'¦s mean duration of employment weeks is any greater than the mean duration of employment weeks within the rest of California.

d. Is there a relationship between the age of a newly employed individual and the number of weeks of employment?

By using a scatter plot and plotting the number of weeks employed in respect to the ages of the workers, you can see that the points are distributed along a straight line. The number of weeks employed increase positively as the age of the worker increases. Therefore it is safe to say that there is a positive correlation between the ages of newly employed workers and the number of weeks they are employed.

Textbook Exercise 7.6, The Trash Bag Case

Text Problem 7.6:

n = 40

mean = 50.575

std dev. = 1.6438

a.

95% = 0.509408783 m = 50.06559122

m = 51.08440878