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