Question

In May 2008, the U.S. government began mailing out tax rebate checks to most Americans in order to stimulate the economy. A Zogby poll of 7815 adults found that only 17% planned to splurge on something they wouldn't normally buy. Men in the sample had higher rate of planned splurging, 20%, and young people (ages 18-24) had an even higher rate of planned splurging of 24%. The pollsters noted that the 17% point estimate had a margin of error of 1.1%, but that the point estimates for subgroups had larger margins of error.

a. What confidence level is the pollster using?

b. Assume that 3805 of the people sampled were men. Determine the margin of error for this subgroup under the confidence level from part (a)

c. Assume that 1328 of those sampled were young. Determine the margin of error for this subgroup under the confidence level from part (a)

Answer 1

A)

We need to use standard normal z table here as the sample sizes are large enough

P = 0.17

N = 7815

Margin of error (MOE) = 0.011 (1.1%)

MOE = Z*√P*(1-P)/√N

after substitution

Z = 2.59

From z table, p(z<-2.59) = P(z>2.59) = 0.005

That is confidence level is 1 - (2*0.005) = 0.99

= 99% confidence level

B)

Here P = 0.17

N = 3805

Z = 2.58

Margin of error = 0.01571107429 ~ 1.57%

C)

N = 1328

After substitution

MOE = 0.02659403128 ~ 2.659%