Question

For the record, this is a homework question, not a test question. The most recent Franklin and Marshall poll of 545 PA registered voters (256 Democrats, 213 Republicans, and 76 Independents) shows that 50% are likely to vote for Bob Casey for Senate and that 33% are likely to vote for his challenger Lou Barletta. a) (2 points) Does the CLT hold in order to use the normal distribution to calculate a 97% confidence interval for the population proportion of voters likely to vote for Bob Casey? Provide evidence to support your answer. b) (8 points) Assume the CLT holds and calculate the 97% confidence interval for the population proportion of voters likely to vote for Bob Casey. c) (8 points) Assume the CLT holds and calculate the 97% confidence interval for the population proportion voters likely to vote for Lou Barletta. d) (2 points) Can we statistically say that Bob Casey is ahead of Lou Barletta? Why or why not?

Answer 1

Here n=545 and we see that np>10 & nq>10.

a. As per CLT n>30 or population needs to ne normal

As n=545, CLT holds

z value for 97% CI is 2.171 as P(-2.171<z<2.171)=0.97

Here p=0.50

So Margin of Error is

So CI is

b.As it is given that CLT holds we will use normal distribution and compute same as a.

z value for 97% CI is 2.171 as P(-2.171<z<2.171)=0.97

Here p=0.50

So Margin of Error is

So CI is

c.Here p=0.33, but n>30 so CLT holds

So Margin of Error is

So CI is

As we see that population propotion of Bob Casey have the range of 0.4535 to 0.5465 but for Lou Barletta population proportion lies in the range of 0.263 to 0.3737

Hence we conclude that Bob Casey is ahead of Lou Barletta