Question

Note that the book states to use a value of 25% if you don’t know what a good value is for the population estimate. Would we want to use this value in planning election polling? Why or why not? What would be the sample sizes needed to get a 95% confidence interval of plus or minus 3% given that the initial estimate of the population proportion is either 1%, 25%, 50%, 75% or 99% (calculate the five intervals). What do you notice that is interesting?

Answer 1

(a)

For p = 0.01:

= 0.05

From Table, critical values of Z = 1.96

e = 0.03

Sample Size (n) is given by:

(b)

For p = 0.25:

= 0.05

From Table, critical values of Z = 1.96

e = 0.03

Sample Size (n) is given by:

(c)

For p = 0.50:

= 0.05

From Table, critical values of Z = 1.96

e = 0.03

Sample Size (n) is given by:

(d)

For p = 0.75:

= 0.05

From Table, critical values of Z = 1.96

e = 0.03

Sample Size (n) is given by:

(e)

For p = 0.99:

= 0.05

From Table, critical values of Z = 1.96

e = 0.03

Sample Size (n) is given by:

Interesting to note is:

for p = 50%, n = 1068 is the highest sample size. The sample size reduces as p deviates from 0.50.