Question

A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.01 level of significance, test the claim that at least half of all voters prefer the Democrat.
State the Test Statistics.

Answer 1

Answer: We will not accept the null hypothesis.

Step-by-step explanation:

Since we have given that

sample size n = 1068

$\hat{p}$ = 48% = 0.48

At 0.01 level of significance, z = - 2.58

Hypothesis are:

$H_0:p=0.5\\\\H_a:p\neq 0.5$

So, test statistic value would be:

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.48-0.50}{\sqrt{\dfrac{0.5\times 0.5}{1068}}}\\\\z=\dfrac{-0.02}{0.0152}\\\\z=-1.315$

So, test statistic > critical value.

Hence, we will not accept the null hypothesis.