Question

Gun rights vs. gun control: In a December 2014 report, "For the first time in more than two decades of Pew Research Center surveys, there is more support for gun rights than gun control." According to a Pew Research survey, 52% of Americans say that protecting gun rights is more important than controlling gun ownership. Gun rights advocates in a conservative city believe that the percentage is higher among city residents.

They survey 200 city residents and find that 130 say that protecting gun rights is more important than controlling gun ownership. What is the test statistic?
Z = -3.68
Z = 3.68
Z = -3.85
Z = 3.85

Answer 1

The right answer is "z = 3.68".

Explanation:

Given that,

p = 52%

or,

= 0.52

n = 200

`\hat{p}= (130)/(200)`

`= 0.65`

Now

The test statistic will be:

⇒
`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n) } }`

On substituting all the given values, we get

⇒
`=\frac{0.65-0.52}{\sqrt{(0.52(1-0.52))/(200) } }`

⇒
`=\frac{0.13}\sqrt{{(0.52* 0.48)/(200) }}`

⇒
`=(0.13)/(√(0.001248) )`

⇒
`=3.68`