# 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.