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

Explanation:

Test statistic for proportion:

`z=\frac{\hat{p}-p}{\sqrt{(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=\frac{0.86-0.94}{\sqrt{(0.94(1-0.94))/(1004)}}\\\\=\frac{-0.08}{\sqrt{(0.0564)/(1004)}}\\\\=(-0.08)/(√(0.0000561752988048))\\\\=(-0.08)/(0.00749501826581)\\\\=-10.673756509\approx-10.67`

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