A large university is well known for both its architecture school and its mechanical engineering program. The dean of the career services office is trying to find whether there is a difference in starting job salary between recently graduated architecture majors and mechanical engineering majors. The starting annual salaries for a random sample of 10 architecture majors and 10 mechanical engineering majors from the most recent graduating class are recorded. Assume that the population variances of the architecture majors' starting salaries and of the mechanical engineering majors' starting salaries are not equal and that the starting salaries for both majors are normally distributed. Let the architecture majors' salaries be the first sample, and let the mechanical engineering majors' salaries be the second sample.
The dean conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence of a difference in average annual starting salary.
For this test: H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.
The test results are: t≈−2.68 , p-value is approximately 0.021
Which of the following are appropriate conclusions for this hypothesis test? Select all that apply.
Select all that apply:
There is sufficient evidence at the 0.05 level of significance to conclude that there is a difference in average annual starting salary between architecture majors and mechanical engineering majors.
There is insufficient evidence at the 0.05 level of significance to conclude that there is a difference in average annual starting salary between architecture majors and mechanical engineering majors.
Reject H0.
Fail to reject H0.
To test that there is evidence of a difference in average annual starting salary.
H_{0} : μ1 = μ2 ; H_{a} : μ1 ≠ μ2
Test statistic,
t ≈ −2.68
p-value = 0.021
Decision:-
If p-value < α (level of significance)
Then we reject H_{0} Otherwise we Accept H_{0}
Here p-value = 0.021 < α = 0.05
Therefore we Reject H_{0}
Conclusion:-
There is sufficient evidence at the 0.05 level of significance to conclude that there is a difference in average annual starting salary between architecture majors and mechanical engineering majors.
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