Question

A box contains a large number of red and blue tickets; the proportion of red tickets is known to be 50%. A simple random sample of 100 tickets is drawn from the box. Say whether each of the following statements is true or false, and explain briefly.

a. The percentage of red tickets in the sample has an expected value of 50%, and an SE of 5%.

b. The 5% measures the likely size of the chance error in the 50%.

c. The proportion of reds in the sample will be around 50%, give or take 5% or so.

d. An approximate 95%-confidence interval for the proportion of reds in the sample is 40% to 60%.

e. There is about a 95% chance that the proportion of reds in the sample will be in the range from 40% to 60%.

Answer 1

Ans:

a)True

mean=0.5

standard error=sqrt(0.5*(1-0.5)/100)=0.05

b)False,as 5% error is in sample proportion,not in population proportion.

c)False,we are not given sample proportion,so we can't say this.

d),e)False,we are not given sample proportion to calculate CI