Question

A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%. The test statistic is a.1.44. b.1.25. c..95. d..80.

Answer 1

a. 1.44

Explanation:

We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%.

At the null hypothesis, it is tested if the proportion is of at most 40%, that is:

`H_0: p \leq 0.4`

At the alternative hypothesis, it is tested if the proportion is of more than 40%, that is:

`H_1: p > 0.4`

The test statistic is:

`z = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that
`p = 0.4, \sigma = √(0.4*0.6)`

A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A.

This means that:

`n = 200, X = (90)/(200) = 0.45`

Value of the test statistic:

`z = (X - \mu)/((\sigma)/(√(n)))`

`z = (0.45 - 0.4)/((√(0.4*0.6))/(√(200)))`

`z = 1.44`

Thus the correct answer is given by option a.