Question

A group of 54 computer science students were taught introductory computer programming class with an innovative teaching method that used a graphical interface and drag-and-drop methods of creating computer programs. At the end of the class, 43 of these students said that they felt confident in their ability to write computer programs. Another group of 43 students were taught the same material using a standard method. At the end of class, 25 of these students said they felt confident. Assume that each class contained a simple random sample of students. Let pX represent the population proportion of students taught by the innovative method who felt confident and let pY represent the population proportion of students taught by the standard method who felt confident. Find a 99% confidence interval for the difference pX−pY . Round the answers to four decimal places.

The 99% confidence interval is ( , )

Answer 1

Here, , n1 = 54 , n2 = 43
p1cap = 0.796 , p2cap = 0.581

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.796 * (1-0.796)/54 + 0.581*(1-0.581)/43)
SE = 0.0931

For 0.99 CI, z-value = 2.58
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.796 - 0.581 - 2.58*0.0931, 0.796 - 0.581 + 2.58*0.0931)
CI = (-0.0252 , 0.4552)