Question

Claim: Fewer than 92% of adults have a cell phone. In a reputable pool of 1015 adults, 83% said that they have a cell phone. Find the value of the test statistic.The value of the test statistic isRound to two decimal places as needed)

Answer 1

Answer:

z=-10.57

Explanation:

The test statistic for a population proportion is given by:

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\text{ where }\begin{cases}p=population\text{ proportion} \\ \hat{p}=\text{sample proportion} \\ n=\text{sample size}\end{cases}$

In the given problem, the parameters are:

• n=1015

,

• p(hat)=83%=0.83

,

• p=92%=0.92

Substitute into the formula above:

$\begin{gathered} z=\frac{0.83-0.92}{\sqrt[]{\frac{0.92(1-0.92)}{1015}}}=\frac{-0.09}{\sqrt[]{\frac{0.92\times0.08}{1015}}} \\ z=-10.57 \end{gathered}$

The value of the test statistic is -10.57 (correct to 2 decimal places).