The following Excel table is the result of a study by MBA students to see if the
ID: 2906869 • Letter: T
Question
The following Excel table is the result of a study by MBA students to see if the average commuting times from suburbs to down town Chicago is any different in the winter. At the .05 level of significance, can it be concluded that the commuting times are different in the winter?
Winter
Spring , Summer, Fall
Mean
38.2 minutes
32.5 minutes
Known Variance
82.81
51.84
Observations
40
40
Hypothesized Mean Difference
0
0
Z
4.50
P(Z<=z) One-tail
.004
Z Critical one-tail
1.645
P(Z<=z) Two-tail
.008
Z Critical two-tail
1.96
Winter
Spring , Summer, Fall
Mean
38.2 minutes
32.5 minutes
Known Variance
82.81
51.84
Observations
40
40
Hypothesized Mean Difference
0
0
Z
4.50
P(Z<=z) One-tail
.004
Z Critical one-tail
1.645
P(Z<=z) Two-tail
.008
Z Critical two-tail
1.96
Explanation / Answer
Claim: The commuting times are different in the winter.
The null and alternative hypothesis is
H0: The commuting times are the same in the winter.
H1: The commuting times are different in the winter.
Level of significance = 0.05
Our hypothesis is a two-tailed test.
P-value = 0.008 ( Using result)
P-value < 0.05 we reject null hypothesis.
Conclusion: The commuting times are different in the winter.