Question

{Exercise 5.57} 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 (Complete Tax website, November 9, 2012). Age 18-34 35-44 45-54 55-64 65+ Online Tax Program(%) 16 12 18 8 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 that 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 that 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 that use an online tax program to prepare their federal income tax return?. 1250 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 that uses an online tax program (to 2 decimals)? 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 that uses an online tax program(to 2 decimals)?

Answer 1

A

Let the no. of people sampled be x.
p = 16%

We need the expected no. of people to be atleast 25.
Thus, x*0.16 = 25
x = 156.25
Hence, we need to sample 157 people.

B

Let the no. of people sampled be x.
p = 12%

We need the expected no. of people to be atleast 25.
Thus, x*0.12 = 25
x = 208.33
Hence, we need to sample 209 people.

C

Let the no. of people sampled be x.
p = 2%

We need the expected no. of people to be atleast 25.
Thus, x*0.02 = 25
x = 1250
Hence, we need to sample 1250 people.

D

Std Dev = [157*0.16*(1-0.16)]^0.5 = 4.5936

E

Std Dev = [209*0.12*(1-0.12)]^0.5 = 4.6979

Answer 2

A

Let the no. of people sampled be x.
p = 16%

We need the expected no. of people to be atleast 25.
Thus, x*0.16 = 25
x = 156.25
Hence, we need to sample 157 people.

B

Let the no. of people sampled be x.
p = 12%

We need the expected no. of people to be atleast 25.
Thus, x*0.12 = 25
x = 208.33
Hence, we need to sample 209 people.

C

Let the no. of people sampled be x.
p = 2%

We need the expected no. of people to be atleast 25.
Thus, x*0.02 = 25
x = 1250
Hence, we need to sample 1250 people.

D

Std Dev = [157*0.16*(1-0.16)]^0.5 = 4.5936

E

Std Dev = [209*0.12*(1-0.12)]^0.5 = 4.6979