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 UPPER bound for a 95% confidence interval for this scenario.

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

Answer 1

For n1 + n2 - 2 = 49 + 38 - 2 = 85 degrees of freedom, we get from the t distribution tables:

P( -1.988 < t85 < 1.988) = 0.95

The standard error now is computed here as:

Now the Upper bound for the 95% confidence interval here is computed as:

Therefore 5.2717 is the required upper limit here.

Therefore 0.7283 is the required lower limit there.