Question

About 72% of 100 randomly sampled MCC students believe they can achieve the American dream and about 62% of 100 randomly sampled Ferris State Universtiy students believe they can achieve the American dream. Construct a 98% 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.

Round to 3 decimal places where appropriate.

If the assumptions are met, we are 98% confident that the difference in the population proportions of MCC and FSU students who believe they can achieve the American dream is between ________ and _________.

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 __________% 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 _______________% will not contain the true population difference in proportions.

Answer 1

Here, , n1 = 100 , n2 = 100
p1cap = 0.72 , p2cap = 0.62

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.72 * (1-0.72)/100 + 0.62*(1-0.62)/100)
SE = 0.0661

For 0.98 CI, z-value = 2.33
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.72 - 0.62 - 2.33*0.0661, 0.72 - 0.62 + 2.33*0.0661)
CI = (-0.054 , 0.254)

If the assumptions are met, we are 98% confident that the difference in the population proportions of MCC and FSU students who believe they can achieve the American dream is between-0.054 and 0.254

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 _98 % 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 2% will not contain the true population difference in proportions.