Question

In the 1992 presidential campaign, H. Ross Perot received about 20% of the popular vote. As the 1996 campaign approached, a statistician wanted to test whether Perot had maintained the same level of support. He polled 100 people and found that 15 of them supported Perot. He will use a .01 level of significance. What is the value of the test statistic?

a. –1.40
b. –1.25
c. 1.25
d. 1.40

Answer 1

The correct option is b.

Explanation:

Given information:

Population proportion = 20% = 0.2

Sample proportion =
`(15)/(100)=0.15`

Sample size = 100

Let as assume that the sample is normally distributed.

The formula for test statistics is

`z=\frac{p-P}{\sqrt{(PQ)/(n)}}`

where,

p is sample proportion.

P is population proportion.

Q is 1-P

n is sample size.

The value of the test statistic is

`z=\frac{0.15-0.2}{\sqrt{(0.2(1-0.2))/(100)}}`

`z=(-0.05)/(0.04)`

`z=-1.25`

The value of test statistic is -1.25. Therefore the correct option is b.