Payroll Statistics Case Study

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 ¡V 8.76 = 28.99 to
= 1.6438

a.
95% = 0.509408783 m = 50.06559122 m = 51.08440878 99% = 0.669478969 m = 49.90552103 m = 51.24447897

b. Yes, we can be 95% confident that the trash bags are at least 50 pounds in strength because the lower confidence level is slightly more than 50 at 50.06 pounds.

c. No, we can not be 99% confident that the trash bags are at least 50 pounds in strength because the lower confidence level is slightly less than 40 at 49.9 pounds.

d. Even though I can not say for sure with 99% confidence that the trash bags have a 50 pound strength, the lower confidence level is very close at 49.9 pounds. Since no other trash bag on the market has a breaking strength of 50 pounds, I think that I can say in good confidence that this bag is the strongest bag on the market.

Textbook Problem 8.76:

a. ,do not reject, the manufacturer¡¦s claim is true , reject the null, the manufacturer¡¦s claim is false

b. Sample size is > 30 so therefore we can use z-statistics. (316/400 ¡V 0.95)/[0.95*(1-0.95)/400]1/2 = -14.683

So, if given a significant level (Ą), if z-stat < -ZĄ, then reject null hypothesis and accept alternative hypothesis.

a -ZĄ Action on null hypothesis
0.10 -1.282