Question

A study is to be conducted to see how long it takes for a taxpayer to complete his income tax return. Assume that the time required to complete the return is normally distributed.
A random sample of 17 taxpayers is taken whose mean (of the time in hours to complete the return) is 7.8 hours with a standard deviation of 2.3 hours.
A) Determine the value of t
B) Find the approximate error
C) Find the interval with 95% confidence for the true mean of the time required to complete the tax return.
All work must appear to receive credit

Answer 1

Solution :

Given that,

= 7.8

s =2.3

n =17

Degrees of freedom = df = n - 1 =17 - 1 = 16

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,16 = 2.120 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.120* ( 2.3/ 17)

= 1.1826

The 95% confidence interval estimate of the population mean is,

- E < < + E

7.8 - 1.1826< < 7.8+ 1.1826

6.6174 < < 8.9826

( 6.6174 , 8.9826)