Question

About 76% of MCC students believe they can achieve the American dream and about 61% of Ferris State Universtiy students believe they can achieve the American dream. Construct a 99% confidence interval for the difference in the proportions of Montcalm Community College students and Ferris State University students who believe they can achieve the American dream.

There were 100 MCC students surveyed and 100 FSU students surveyed.

a. With 99% confidence the difference in the proportions of MCC and FSU students who believe they can achieve the American dream is _______ (round to 3 decimal places)

and _______ (round to 3 decimal places).

b. If many groups of 100 randomly selected MCC students and 100 randomly selected FSU students were surveyed, then a different confidence interval would be produced from each group. About _______ percent of these confidence intervals will contain the true population proportion of the difference in the proportions of MCC students and FSU students who believe they can achieve the American dream about ________ percent will not contain the true population difference in proportions.

Answer 1

(b)  If many groups of 100 randomly selected MCC students and 100 randomly selected FSU students were surveyed, then a different confidence interval would be produced from each group. About 99 percent of these confidence intervals will contain the true population proportion of the difference in the proportions of MCC students and FSU students who believe they can achieve the American dream about 1 percent will not contain the true population difference in proportions.

(a) na (100-99)'%. Za12 20.005 - 2.576, =1% -0.01 ni = n2= 100, pi= 0.76, pê 0,61. (a) 99% eI for b-b2 = ê -²) + Zarza ê (1-62 + 19 (1 ) ni 10.317 12 0.017 and