The University of Ottawa is interested in offering its employees
one of two employee
benefit packages. A random sample of the university’s employees is
collected, and each
person in the sample is asked to rate each of the two packages on
an overall preference
scale of 0 to 100. The results are
package A: 45, 67, 63, 50, 77, 60, 47, 39, 56, 68, 70
package B: 56, 79, 60, 45, 85, 39, 50, 41, 50, 69, 82
After analyzing the data, the University concludes that its
employees prefer, on
average, one package over the other, i.e., there is a significant
difference between the
two packages, at significance level = 0:05.
True False
Solution : False
Explanation :
Let ,The random sample of Package A and Package B
Hypothesis :
Null Hypothesis : Mean difference of two packages are equal.
Alternative Hypothesis : Mean difference of two packages are not equal.
Mathematically :
Where and are the mean of package A and package B respectively.
Test Statistic:
Here we have sample size is 11 and Population standard deviation not know so we use "T - test"
Where S = Pooled standard deviation
n1 , n2 are sample sizes and
and are sample means
s = 14.5346
Test statistic becomes;
Critical T :
From T table :
Criteria : If |t| < tcrit , then accept the null hypothesis at level of significance.
So here 0.21 < 2.086 , we may accept the null hypothesis at 5% level of significance.
Conclusion :
The average of package A does not differ to average of package B
So there is no significant difference between two packages.
Minitab Output (for reference) :
Two-Sample T-Test and CI: A, B
Two-sample T for A vs B
N Mean StDev SE Mean
A 11 58.4 12.0 3.6
B 11 59.6 16.7 5.0
Difference = μ (A) - μ (B)
Estimate for difference: -1.27
95% CI for difference: (-14.20, 11.66)
T-Test of difference = 0 (vs ≠): T-Value = -0.21 P-Value = 0.839 DF
= 20
Both use Pooled StDev = 14.5346
The University of Ottawa is interested in offering its employees one of two employee benefit packages....
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