4. A ?2 test to determine whether the sample is significantly different from the expected distribution would be most appropriate. The data in this case yield ?2 = 2.51, below the critical value cutoff for ? = 0.05. We can assume that the sample is NOT significantly different from the general population.

5. In this data, there appears to be no gender-based difference between the way in which people commute to work. Since ?2 = 7.715, df = 3 and p > 0.1, this data fails to exceed the critical ?2 value for the analysis, 7.81.

6. To test this hypothesis I will use a t-test of means. Critical t-value for ? = 0.05 is (conservatively!) 1.98.

T = (M1 - M2) / SE (M1 - M2)

SE = ( (var1/n1) + (var2/n2) = ( (0.52/100) + (0.62/64) = 0.09

T = 1 / 0.09 = 11.11

According to this analysis it appears that there is a significant difference between loan repayment rates through Savings & Loan institutions and other institutions, at least in this sample.

7.

Region

Manager Rating

Region

Manager Rating

West1

74

81

West2

88

63

West3

78

56

West4

85

68

West5

Managers in the eastern region are rated significantly lower than managers in the western region according to this sample.
8. These data do not indicate a significant difference between Variable 1 and Variable 2 unless a looser criterion for significance (? = 0.10) is used, even in the one-tailed case. One-tailed t-tests should only be used when they can be theoretically justified, i.e. If the values being measured could not possibly cause one group's scores to be lower than the other's, but only equal. However, there is a small-to-medium correlation between the variables, so they may not be independent. If not, this violates the assumptions underlying the t-test, and a different analysis (perhaps based on regression) should be used.