Question

According to the Internal Revenue Service, 80% of all tax returns lead to a refund. A random sample of 100 tax returns is taken, and it was found that 83% of the tax returns in the sample require a refund. Using the sampling distribution of the proportion, calculate the probability that the sample proportion exceeds 85% in the sample of 100 tax returns?

a. 0.1056

b. 0.2266

c. 0.2972

d. 0.0916 30.

In a small town, there are 3,000 registered voters. An editor of a local newspaper would like to predict the outcome of the next election. In particular, he is interested in the likelihood that Eli Brady will be elected. The editor believes that Eli, a local hero, will be supported by 54% of votes. A poll of 500 registered voters is taken. Assuming that the editor’s belief is true, find the standard error of the proportion of voters in favor of Eli Brady?

a. 0.0223

b. 11.1445

c. 0.0204

d. 0.0091

Answer 1

Solution

1) Given that,

p = 0.80

1 - p = 1 - 0.80 = 0.20

n = 100

= p = 0.80

=  [p( 1 - p ) / n] = [(0.80 * 0.20) / 100 ] = 0.04

P( > 0.85) = 1 - P( < 0.85 )

= 1 - P(( - ) / < (0.85 - 0.80) / 0.04)

= 1 - P(z < 1.25)

Using z table

= 1 - 0.8944

= 0.1056

correct option is = a

2) Given that,

p = 0.54

1 - p = 1 - 0.54 = 0.46

n = 500

= p = 0.54

=  [p( 1 - p ) / n] = [(0.54 * 0.46) / 500 ] = 0.0223

correct option is = a