The following table shows the percentage of individuals in each age group who use an online tax program to prepare their federal income tax return (CompleteTax website, November 9, 2012). Age Online Tax Program (%) 18–34 16 35–44 12 45–54 10 55–64 8 65 + 2 Suppose a follow-up study consisting of personal interviews is to be conducted to determine the most important factors in selecting a method for filing taxes. a. How many 18–34-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return? b. How many 35–44-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return? c. How many 65+-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return? d. If the number of 18–34-year-olds sampled is equal to the value identified in part (a), what is the standard deviation of the percentage who use an online tax program? e. If the number of 35–44-year-olds sampled is equal to the value identified in part (b), what is the standard deviation of the percentage who use an online tax program?

Find the number of 18-34 year olds that must be sampled to obtain the expected number of at least 25 who use an online tax program to prepare their federal income tax return.

Explanation of Solution

Calculation:

The data represents the percentage of individuals in each age who use an online tax program to prepare their federal income tax return. Personal interviews are conducted to determine the most important factors in selecting a method for filing taxes.

The formula for the mean of a binomial random variable is,

E(X)=np

The expected number of individuals who use an online tax program to prepare their federal income tax return is at least 25. That is,

E(X)=np≥25

Substitute the value p=0

Answer 7

b.

To determine

Find the number of 35-44 year olds that must be sampled to obtain the expected number of at least 25 who use an online tax program to prepare their federal income tax return.

Answer 8

c.

To determine

Find the number of 65 and more year olds person, that must be sampled to obtain the expected number of at least 25 who use an online tax program to prepare their federal income tax return.

Answer 9

d.

To determine

Compute the standard deviation of the percentage who use an online tax program if the number of 18-34 year olds sampled is equal to the value identified in part (a).

Answer 10

e.

To determine

Compute the standard deviation of the percentage who use an online tax program if the number of 35-44 year olds sampled is equal to the value identified in part (b).

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Solutions

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Explanation of Solution

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Age	Online Tax Program (%)
18–34	16
35–44	12
45–54	10
55–64	8
65 +	2