Question

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two candidate election, if a specific candidate receives at least 54% of the vote sample, that candidate will be forecast as the winner. You select a select a random sample of 100 voters. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1?

What is the probability that a candidate will forecast as winner when the population percentage of her vote is 56%?

What is the probability that a candidate will forecast as winner when the population percentage of her vote is 49%

Suppose the sample size was increased to 400. Repeat the process using th new sample size.

Answer 1

n=100

a)mean=np=100*50.1/100=0.501

sd=sqrt(np(1-p))=sqrt(100(0.501*0.46)=sqrt(24.99)=4.9999

assume normal distribution

Z=(54-50.1)/4.99999=0.7800

P(Z>0.78)=0.21770

b)Find mean and sd using 56 %
mean=100*0.56=56

sd=sqrt[(100(0.56)(0.44)]=sqrt(24.64)=4.9638

Z=(54-56)/4.9638=-0.4029

P(Z>-4029)=1-P(Z<0.4029=1-0.34458=0.6565

c)Find mean and sd using 49%

mean=49

sd=sqrt(100(0.49*0.51)=4.9989

Z=(54-49/4.9989)=1.0002

P(Z>1.0002)=1.-0.8414=0.1586

d)the sample size was increased to 400. Repeat the process using the new sample size.

please take n=400 calculate a to c again