Question

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). Excel File: data05-65.xls Online Tax Program (%) Age 18-34 35-44 45-54 55-64 65+ 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? (Round to the nearest next whole number) 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? (Round to the nearest next whole number) 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? (Round to the nearest next whole number) 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) number to be sampled =25/0.16=156.25 ~ 157

b)

number to be sampled =25/0.12=208.33 ~ 209

c)

number to be sampled =25/0.02 =1250 (try 1251 if this comes wrong)

d)

std error of proportion=σp=√(p*(1-p)/n)=

0.0293 ~ 2.93 % ( please try 0.03 if this comes wrong)

e)

std error of proportion=σp=√(p*(1-p)/n)=

0.0225 ~ 2.25 %( please try 0.02 if this comes wrong