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:

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

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

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

The value of the statistic is Z=-10.18