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

z=-10.57

Step-by-step explanation:

The test statistic for a population proportion is given by:

`z=\frac{\hat{p}-p}{\sqrt{(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[]{(0.92(1-0.92))/(1015)}}=\frac{-0.09}{\sqrt[]{(0.92*0.08)/(1015)}} \\ z=-10.57 \end{gathered}`

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