10.7

A company’s auditor believes the per diem cost in Nashville, Tennessee, rose significantly between 1996 and 2006. To test this belief, the auditor samples 51 business trips from the company’s records for 1996; the sample average was $190 per day, with a population standard deviation of $18.50. The auditor selects a second random sample of 47 business trips from the company’s records for 2006; the sample average was $198 per day, with a population standard deviation of $15.60. If he uses a risk of committing a Type I error of .01, does the auditor find that the per diem average expense in Nashville has gone up significantly?

 

n₁ = 51                        n₂ = 47

= 190                       = 198

σ₁ = 18.50                   σ₂ = 15.60

 

σ₁² = 342.25              σ₂² = 243.36
µ₁              µ₂

α = .01

 

This is a one-tailed test.

H₀: µ₁ = µ₂

H_a: µ₁ < µ₂

 

 

 

α = .01

From z-Table:

z_α = -2.33

We will reject the null hypothesis, IF the observed value of the test statistic z is less than -2.33.

 

 

 

 (-2.32) is not less than  (-2.33).  is in the non-rejection region. We do NOT reject the null hypothesis.

 

The per diem cost in Nashville, Tn, did not rise significantly between 1996 and 2006.