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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

Respuesta :

Answer:

The correct option is b.

Step-by-step explanation:

Given information:

Population proportion = 20% = 0.2

Sample proportion = [tex]\frac{15}{100}=0.15[/tex]

Sample size = 100

Let as assume that the sample is normally distributed.

The formula for test statistics is

[tex]z=\frac{p-P}{\sqrt{\frac{PQ}{n}}}[/tex]

where,

p is sample proportion.

P is population proportion.

Q is 1-P

n is sample size.

The value of the test statistic is

[tex]z=\frac{0.15-0.2}{\sqrt{\frac{0.2(1-0.2)}{100}}}[/tex]

[tex]z=\frac{-0.05}{0.04}[/tex]

[tex]z=-1.25[/tex]

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

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