Question

A poll of 1000 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, do the data provide sufficient evidence to conclude that the percentage of voters who prefer the Democrat is less than 50%?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.5
Alternative Hypothesis, Ha: p < 0.5

single proprotion z test

.05 is level of significance

2)

• The sample must be reasonably random
• The sample must be less than 10% of the population
• The sample must be large enough so that:
n• pˆ and n(1 - pˆ ) ≥ 10 for a confidence interval
n• p and n(1 - p) ≥ 10 for the significance test

3)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.48 - 0.5)/sqrt(0.5*(1-0.5)/1000)
z = -1.26

P-value Approach
P-value = 0.1038

4)

As P-value >= 0.05, fail to reject null hypothesis.

5)

There is not sufficient evidence to conclude that the percentage of voters who prefer the Democrat is less than 50%