Question

1. A poll was taken of UW students to estimate the proportion of all students that believe the Husky men’s basketball team will beat Oregon at the upcoming game on 18 January. A random sample of 1,000students was selected, and via an emailed survey link, students were simply asked, Yes or No, if they thought the Huskies would win the game. Of the 1,000 students that were emailed, 200 chose not to answer. Of those that answered, 623 believe the Huskies will win.
2. 1. a) What is the sample size for the survey?
   2. b) What sample size would be needed to reduce the margin of error by one-half?

Answer 1

A random sample of 1,000students was selected

Of the 1,000 students that were emailed, 200 chose not to answer.

Thus Students who choose to answer are 800   ( 1000 - 200 )

Of those that answered, 623 believe the Huskies will win.

Number of students who believe Oregon will win are 177 ( 800 -623 )

a) What is the sample size for the survey?

Sample size of survey is 1000

Initial A random sample of 1,000 students was selected .

But 200 of them chose not to answer

So there are 20 % of people who do not responded .

If we assume we need minimum 1000 responses who say YES OR NO and also 20% of popuation is not going to respond

New required sample size would be

                 Final sample size = Effective sample size/ (1- non response rate anticipated)

                                                Here non response rate anticipated is 0.2 or 2%

                                             = 1000 / ( 1 - 0 .2)

                                             = 1250

Thus if we want minimum of 1000 responses who say YES OR NO , then we should take sample survey of size 1250

b)

The smaller the sample size is, the larger the margin of error.

To keep the same margin of error at a higher level of confidence, we would need to increase our sample size.

In order to cut the margin of error in half, we would have to quadruple our sample size. Doubling the sample size will only decrease the original margin of error by about 30%.

The relationship between the sample size and the margin of error is an inverse square root relationship. That means if you want to cut your margin of error in half, you need to quadruple your sample size .

Let E be the Error , and n be the sample size then

E = Z_α/2 / n^1/2

This gives us the formula n =   ( Z_α/2 / E )².

So we need to increase our samples size i.e 4 times of initial samples size

Sample size may increase up to four thousand samples .