# Margin of Error

Question

Assume that the students who completed the M&Ms survey in a previous semester represent a random sample of all students at the University. In that sample, we found that 84 had even IDs out of the 201 students.

a) Calculate the sample proportion of students with an even ID.

b) Construct a 95% CI for the proportion of students with even IDs.

c) Interpret the interval above.

d) What size sample would be needed to ensure the margin for error is no more than 3% each way with 98% confidence?

Question

In a random sample of 100 customers in ―The Olde Coffee Shoppe‖, 25 paid by credit card.

a) Find a 90% confidence interval for the proportion of all customers who pay by credit card. Interpret this interval.

b) Find a 95% confidence interval for the proportion of all customers who pay by credit card.

c) Suppose instead that the sample had been 60 people with 15 using their credit card. Now calculate the 90% and the 95% confidence intervals for the population proportion.

d) Compare the four confidence intervals and comment on the results.

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