Question

8.1.14Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1194 adults, 87% said that they have a cell phone. Find the value of the test statistic.The value of the test statistic is(Round to two decimal places as needed.)

Answer 1

The claim states that "the population proportion of adults that has a cell phone is less than 94%"

The parameter of interest is the population proportion, symbolized as p

The claim is then

`p<0.94`

A sample of n=1194 and a sample proportion of p'hat=0.87 was obtained.

The test statistic you have to use to prove the claim is an approximation to the standard normal distribution:

`Z=\frac{p^(\prime)\text{hat-p}}{\sqrt[]{(p(1-p))/(n)}}\approx N(0,1)`

Replace the formula with the given values of the proportions and sample size to determine the value of the statistic under the null hypothesis:

`\begin{gathered} Z=\frac{0.87-0.94}{\sqrt[]{(0.94(1-0.94))/(1194)}} \\ Z=\frac{-0.07}{\sqrt[]{(0.0564)/(1194)}} \\ Z=-10.18 \end{gathered}`

The value of the statistic is Z=-10.18