An Insurance Company Is Considering Opening a New Branch in Lansing

An insurance company is considering opening a new branch in Lansing. The company will choose the final location from two locations within the city. One of the factors in the decision is the annual family income (in thousands of dollars) of five families randomly sampled from a radius of five miles from the potential locations. Perform equal-variances t-test at the 5% significance level to determine whether the population means differ.
What is the t-statistic?
______________
Reject Region: Reject H0 if |t| > ______________
Conclusion: ______________
The population means ______________ differ.
Perform an F-test for one-way ANOVA at the 5% level of significance to determine whether the population means differ.
What is the F-statistic?
______________
Reject Region: Reject H0 if |F| > ______________
Conclusion: ______________
The population means ______________ differ.
What is the relation between the observed t and observed F test statistics from the previous two questions?
F = ______________
Does the same relation hold true for the corresponding critical values?
______________
If we want to determine whether the population mean income for area 2 is higher than that for area 1, can we still use both the t and F -tests applied in the previous questions?
______________
Explain.
______________