posted by JJ on .
A national opinion poll found that 44% of all American adults agree that parents should be given vouchers good for education at any public or private school of their choice. Suppose that in fact the population proportion who feel this way is p=0.44.
A) Many opinion polls have a "margin of error" of about plus or minus 3%. What is the probability that an SRS of size 300 has a sample proportion p-hat that is within plus or minus 3%(plus or minus .03)of the population proportion p=.44? (show how you would do it using a graphing calculator)
b) Answer the same question for SRSs of sizes 600 and 1200. What is the effect of increasing the size of the sample?
I need the work shown but the answers are:
a) Find P(0.41 ¡Ü p(hat) ¡Ü 0.47)=P(123 ¡Ü X ¡Ü 141. Software gives 0.7309.
b) For n=600, software gives 0.8719. For n=1200, software gives 0.9663. Larger sample sizes are more likely to produce values of p-hat close to the true value of p.