Statistics

Case Study-1

AgeWeeks Employed

5521

3018

2311

5236

4119

2512

427

4525

256

4021

2513

2511

5934

4927

3318

3520

a.

AgeWeeks Employed

Mean37.75Mean18.6875

Standard Error2.974195Standard Error2.

188452

Median37.5Median18.5

Mode25Mode21

Standard Deviation11.89678Standard Deviation8.753809

Sample Variance141.5333Sample Variance76.

62917

Kurtosis-1.17143Kurtosis-0.21626

Skewness0.337402Skewness0.522601

Range36Range30

Minimum23Minimum6

Maximum59Maximum36

Sum604Sum299

Count16Count16

Confidence Level(99.0%)8.

764138Confidence 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

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 Riversides 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% =0.509408783m =50.06559122

m =51.08440878

99% =0.669478969m =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 manufacturers claim is true

, reject the null, the manufacturers 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)/4001/2 = -14.683

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

a-ZNAction on null hypothesis

0.10-1.282Reject

0.05-1.

645Reject

0.01-2.326Reject

0.001-3.090Reject

From the above information it can be concluded that the manufacturers claim is false.

c.

Not really because the manufacturer claims that their television sets last at least 5 years without needing repairs but the sample collected was from consumers that owned their sets for 5 years and not beyond. In order for the results of the survey to have practical importance we would need to sample consumers that have owned their sets for 5 or more years.

Palmer vs. Woods:

Woods,1999 Palmer,1960

mean =69.56mean =69.95

N=84N=112

std dev.

=2.5std dev. =2.5 .