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.
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.
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,
The expected number of individuals who use an online tax program to prepare their federal income tax return is at least 25. That is,
Substitute the value
b.
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.
c.
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.
d.
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).
e.
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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