Introduction and Summary REVISED

Forty random numbers were generated using anonline random number generator and divided into four equalcategories. The mean, standard deviation and sample size of thesecategories were then determined and in turn used to compute thecritical value, margin of error, confidence interval, and pointestimate of the sample using different confidence levels.

Table 1: Sorted Set of Random Data

1

21

39

52

1

21

39

54

4

21

39

55

11

28

44

59

13

29

46

63

16

30

46

63

18

33

48

68

18

34

51

69

19

35

52

70

20

35

52

73

Summary

The point estimate is determined by finding theaverage between the upper bound and lower bound of the confidenceinterval. The confidence level, on the other hand, is directlyproportional to the critical value, which implies that the criticalvalue increases with every increase in the confidence level. Theconfidence interval is determined by finding the difference and sumbetween the mean and the margin of error. The difference between thetwo parameters produces the lower bound of the confidence intervalwhile the sum produces the upper bound. This interval is a range ofvalues that is likely to contain an unknown population parameter. If,for instance, you draw a random sample several times, a certainpercentage of the confidence intervals will contain the populationmean.

Table 2: Important Statistics

Mean

37.25

Standard Deviation

20.0867

Sample Size

40

Population

Sample

Mean

38

37.25

Standard Deviation

21.6

21.6

The population and sample mean are almost equalwhile the standard deviations are identical

Confidence Interval 1

The Critical Value

1.8331

Margin of Error

6.2248

Confidence Interval.

Lower Bound

31.0252

Upper Bound

43.4748

Point Estimate

37.25

Confidence Interval 2

The Critical Value

2.8214

Margin of Error

8.1808

Confidence Interval

Lower Bound

29.0692

Upper Bound

45.4308

Point Estimate

37.25

Reference

Brase, C. H., &amp Brase, C. P. (2012). Understanding basic statistics. Pacific Grove, Calif. : Cengage Learning.