Question

In a poll, 51% of the people polled answered yes to the question "Are you in favor of the death penalty for a person convicted of murder?" The margin of error in the poll was 3%, and the estimate was made with 96% confidence. At least how many people were surveyed? Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). The minimum number of surveyed people was 1. (Round up to the nearest integer.)

Answer 1

1)

Sample size estimation for proportion                              
                              
Preliminary estimate for proportion (Known) = 0.51
Margin of error =E=0.03   
Level of significance =   0.04          
Z critical value is (by using Z table)=2.054          
                              
Sample size
$n=\left [ \hat{p} (1-\hat{p})\right ]\left [ \frac{Z}{E} \right ]^2$

                              
=1171.45
Therefore, sample size approximately was 1171

「2.054] = [0.51(1 -0.51]] 0.03

2)

given a confidence interval (15,27)

point estimate of the population mean = (15+27)/2 = 21

The margin of error = uppper bound - point estimate

= 27 - 21

= 6

3)

given xbar = 120.4

s = 12.9

n = 40

t critical value for 99% confidence with 39 df is = 2.707

$\bar{x}\pm t*\frac{s}{\sqrt{n}}$

120.4 +/- 2.707*12.9/sqrt(40)

120.4 +/- 5.52

lower bound = 114.88

upper bound = 125.92