Question

Q1)In a February 2018 poll 81% of Canadians said that they were watching the Winter Olympic coverage at least part of the time. This poll was base

on 750 randomly sampled Canadians.

a)Check the assumptions and conditions needed for calculating a confidence interval are met. Clearly state the assumptions and conditions.

b)Calculate the margin of error, if you want to be 90% confident of your results. Show your work

C)Calculate a 90% confidence interval. Show your work.

d)Interpret the confidence interval in the context of the problem.

e)Suppose that we want to reduce the margin of error to half of that calculated in Question 2, but keep the confidence level the same. How many individuals should they survey? Justify your answer

Answer 1

Solution:-

1)

a) All the assumptions for calculating the confidence interval are met.

The data are a simple random sample from the population of interest.

The population is at least 10 times as large as the sample.

n⋅p ≥ 10 and n⋅(1−p) ≥ 10, where n is the sample size and p is the true population proportion.

b) 90% margin of error is 0.02356.

M.E = 1.645*0.014325

M.E = 0.02356

c) 90% confidence interval is (0.7864,0.8336).

d) If repeated samples were taken and the 90% confidence interval was computed for each sample, 90% of the intervals would contain the population proportion.

e) The required sample size is 3002.

M.E = 0.02356/2

M.E = 0.01178

n = 3001.0956

n = 3002