Question

Recall the information from above...

When I sit and watch my students take exams, I often think to myself "I wonder if students with bright calculators are impacted by the pretty colors." This leads me to wonder if there is a difference in the exam scores of students with colorful calculators versus the exam scores of students with plain black calculators. To investigate further, I took a sample of past students. There were 49 students with colorful calculators with a mean exam score of 84 and a corresponding standard deviation of 4.7. There were 38 students with plain black calculators with a mean exam score of 87 and a corresponding standard deviation of 5.7. (Calculate differences Black - Colorful.)

Give the LOWER bound for a 95% confidence interval for this scenario.

Answer 1

Mean1 = 87

Sample size1 (n1) = 38

Standard deviation1 (s1) = 5.7

Mean2 = 84

Sample size2 (n2) = 49

Standard deviation2 (s2) = 4.7

Confidence interval(in %) = 95

Since we know that

Required confidence interval = (3.0-2.2173, 3.0+2.2173)

Required confidence interval = (0.7827, 5.2173)

Lower Bound of Confidence Interval = 0.7827

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