Question

A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all voters prefer the Democrat.

State the sample percentage and sample size.

Answer 1

Solution:

Sample size n = 1068

Sample percentage = 48%

i.e. = 48% = 0.48

Claim: at least half i.e. at least 0.5

Use  0.05 level of significance

1)

H₀: p ≥ 0.50

H_a: p < 0.50

2)

The test statistic z is

z =  

=  (0.48 - 0.5)/[0.5*(1 - 0.5)/1068]

= -1.31

3)

Left tailed test

So ,

p value = P(Z < z) = P(Z < -1.31) = 0.0951

p value = 0.0951

4)

Fail to reject H₀

(Because p value is greater than 0.05)

5)

There is not sufficient evidence to reject the claim that at least half of all voters prefer the Democrat.