Question

Claim: Fewer than 94​% of adults have a cell phone. In a reputable poll of 1004 ​adults, 86​% said that they have a cell phone. Find the value of the test statistic.

Answer 1

Answer: The value of test statistic = -10.67

Step-by-step explanation:

Test statistic for proportion:

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

, where p= population proportion

n= sample size

$\hat{p}$ = sample proportion

AS per given,

p=0.94, n= 1004, $\hat{p}=0.86$

$z=\dfrac{0.86-0.94}{\sqrt{\dfrac{0.94(1-0.94)}{1004}}}\\\\=\dfrac{-0.08}{\sqrt{\dfrac{0.0564}{1004}}}\\\\=\dfrac{-0.08}{\sqrt{0.0000561752988048}}\\\\=\dfrac{-0.08}{0.00749501826581}\\\\=-10.673756509\approx-10.67$

i.e. the value of test statistic = -10.67