Undergrad Survey: Normal Distribution, Statistics Problem Example

The undergraduate survey data was analyzed to determine the normal distribution, or lack thereof, for the age, height and GPA data sets.  A total of 50 students were surveyed.  To perform this analysis, the immediate objective was to create a histogram of the data in Excel to effectively use the software to create a normal distribution curve.  Through this simple process, it was found that only the height data held an overall bell curve showing normal distribution.  The overall mean was 67 inches which also holds strong to the middle of the bell curve.

However, age and GPA did not provide a normal distribution.  The age data set created a bell curve with a large curve surrounding the left-side – roughly 20 years old.  This would suggest a normal distribution; however, this data set also contains a large number of individuals older than 24 years of age.  In fact, the mean for this data set was 24.6 years old, which is not in the middle of the bell curve (see chart below).

This clearly shows that the data is not normally distributed.  Furthermore, the GPA distribution curve is not a curve at all.  It actually provides an upwardly mobile linear curve showing that there is no normal distribution for the GPA data set either.

Construct Confidence Interval 95% for GPA

To construct the confidence interval of 95% for the GPA data set we completed the steps as outlined below:

Compute alpha (?): ? = 1 – (Confidence Interval / 100) = 1- (95 / 100) = 0.05

Find the critical probability (p*): p* = 1 – ?/2 = 1 – 0.05/2 = 0.975

Find the degrees of freedom (df): df = n – 1 = 50 – 1 = 49

The critical value is the t score having 49 degrees of freedom and a cumulative probability equal to 0.975. By using a t Distribution Calculator, the critical value is determined to be 2.01.

The range of the confidence interval is defined by our sample statistic + the margin of error.  In this scenario, we chose a sample statistic of 3.01 for the GPA.  The compute the margin of error, we use the following formula:

Margin of Error (ME):  ME = critical value * standard error = 2.01 * 0.95 = 1.91

The range of the confidence interval is defined by the sample statistic + margin of error.  Therefore, the confidence interval of 95% is illustrated as follows:

CI of 95% = 2.01  + 1.91