A survey of 300 students at York University revealed that 112 favour an NDP candidate for M.P.Construct a 98% confidence interval for the percentage of all York University students who favour an NDP candidate.

Question

Quizplus · Accepted Answer

To construct a confidence interval, we use the formula:

CI = p ± z*sqrt((p*(1-p))/n)

where:
p = proportion in the sample who favour an NDP candidate = 112/300 = 0.3733
n = sample size = 300
z* = z-score for a 98% confidence level = 2.33 (from standard normal distribution table)

Plugging these values into the formula, we get:

CI = 0.3733 ± 2.33*sqrt((0.3733*(1-0.3733))/300)
CI = 0.3733 ± 0.0553
CI = (0.3180, 0.4286)
CI = (31.9%, 42.9%)

Rounding to one decimal place, we get choice D) (30.8%, 43.8%) as the closest option. This means we can be 98% confident that the percentage of all York University students who favour an NDP candidate is between 30.8% and 43.8%.

A Survey of 300 Students at York University Revealed That