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 conclusion.

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

Answer 1

Solution:

H0 : p 0.5

H1 : p < 0.5

n = 1068

= 48% = 0.48

The test statistic z is

z = [ - p]/[[p(1-p)/n]

=  (0.48 - 0.5)/[0.5*(1 - 0.5)/1068]

= -1.31

Left tailed test

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

p value is greater than 0.05 level.

Fail to reject H₀

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