3. 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. 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. (1) 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? (2) 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? (3) 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? (4) If the number of 18~34-year-olds sampled is equal to the value identified in part (1), what is the standard deviation of the percentage who use an online tax program? (5) If the number of 35~44-year-olds sampled is equal to the value identified in part (2), what is the standard deviation of the percentage who use an online tax program?

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Asked Nov 17, 2019
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3. 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. 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. (1) 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? (2) 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? (3) 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? (4) If the number of 18~34-year-olds sampled is equal to the value identified in part (1), what is the standard deviation of the percentage who use an online tax program? (5) If the number of 35~44-year-olds sampled is equal to the value identified in part (2), what is the standard deviation of the percentage who use an online tax program?

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Step 2

1)

For age group 18-34 it was found that 16% individual use an online tax program to prepare their federal income tax return. Thus, the probability of success (p) is 0.16.

The formula for the mean of a binomial random variable is E(X) = np.

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

E(X) np
пр 2 25
(By substitute p as 0.16)
n(0.16) 25
n156.25
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E(X) np пр 2 25 (By substitute p as 0.16) n(0.16) 25 n156.25

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Step 3

Thus, the number of 18-34 year old 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 is at least 157.

2)

For age group 35-44 it was found that 12% individual use an online tax program to prepare thei...

Е(x)- пр
пр 2 25
(Ву substitute p as 0.12)
n(0.12) 2 25
п2 208.33
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Е(x)- пр пр 2 25 (Ву substitute p as 0.12) n(0.12) 2 25 п2 208.33

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