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?
State the decision rule. (Round your answer to 3 decimal
places.)
___________
Compute the pooled estimate of the population variance.
(Round your answer to 2 decimal places.)
____________
Compute the test statistic. (Round your answer to 3
decimal places.)
__________
for sales
= 141.83, s1 = 11.2324, n1 = 6
for audit
= 125.57, s2 = 12.5546, n2 = 7
H_{0}:
H_{1}:
A) df = 6 + 7 - 2 = 11
At 0.025 significance level the critical value is t^{*} = 2.201
Reject H_{0}, if t > 2.201
B) The pooled variance(s_{p}^{2}) = ((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_{p}^{2}/n1 + s_{p}^{2}/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.
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