Fifty randomly selected UBC students were asked whether they prefer Translink's new Compass Card bus pass over the U-Pass. From this sample of 50 students, 35 said they prefer Compass Cards.
(a) Find a 95% condence interval for the true proportion of UBC students who prefer the Compass Card.
(Make sure to check any necessary conditions and to state a conclusion in the context of the problem.)
(b) Explain what 95% condence means in this context.
(c) Suppose no prior information about the sample proportion of students who prefer the Compass Card were available. Translink wants to estimate the proportion of students who prefer the Compass Card.
They want the estimate to be correct within 0.04 with 95% condence. Approximately how large a sample would be required?