Question

Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.

Sales ($)	129	135	148	160	135	144
Audit ($)	122	103	127	136	129	120	142

At the 0.025 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff?

1. State the decision rule. (Round your answer to 3 decimal places.)
   ___________
   

2. Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.)
   ____________
   

3. Compute the test statistic. (Round your answer to 3 decimal places.)
   __________

Answer 1

for sales

= 141.83, s1 = 11.2324, n1 = 6

for audit

= 125.57, s2 = 12.5546, n2 = 7

H₀:

H₁:

A) df = 6 + 7 - 2 = 11

At 0.025 significance level the critical value is t^* = 2.201

Reject H₀, if t > 2.201

B) The pooled variance(s_p²) = ((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/(n1 + n2 - 2) = (5 * (11.2324)^2 + 6 * (12.5546)^2)/(6 + 7 - 2) = 143.32

C) The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

= (141.83 - 125.57)/sqrt(143.32/6 + 143.32/7) = 2.441

Since the test statistic is greater than the critical value (2.441 > 2.201), so we should reject the null hypothesis.

So at 0.025 significance level, we can conclude that the mean daily expenses are greater for the sales than the audit staff.