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T-Test and Estimated Normal distribution

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Calculate and Display, using Excel, the following:

1. Draw the statistics as a histogram. Do they resemble the Normal Distribution?
2. Find the median, the average grade and the standard deviation of the two terms.
3. Calculate using the t-student distribution to find out if there is a significant difference among these two terms.

Grade Range Numeric Grade Number of Students in term 1 Number of Students in term 2
Outstanding (A*) 80 + 85 1 1
Excellent (A) 70-79 75 3 4
Very Good (B) 60-69 65 8 7
Good (C) 50-59 55 5 7
Marginal Fail (D) 40-49 45 2 4
Fail (F) Below 40 0 1 2
Total 20 25

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Solution Summary

For a given sample data of students of a class with their grades, some statistical analyses are carried out.

Solution Preview

For calculations see attached xls file.

Q 1. See attachment for histograms. Term 2 distribution is closer to Normal distribution than Term 1.

Q 2.
Median:
Me = L + (n/2 - cfp)*i/fm
L: lower bound of class (or interval) containing median
n = sample size
cfp = cumulative frequency of the class before median class
fm = frequency of median class
i interval of class

Term 1:
Middle ranked candidate (10th+11th)/2 = 10.5 th i.e., class ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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