Question

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: package B: 45, 67, 63, 50, 77, 60, 47, 39, 56, 68, 70 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 a = = 0.05. True False

Answer 1

Run a t-Test: Two-Sample Assuming Equal Variances analysis to conclude there is a significant difference is exists between the variables or not.

1. Bring data in to excel.

2. Go to data tab -- > choose data analysis --> choose t-Test: Two-Sample Assuming Equal Variances

с ? X خ N لا t-Test: Two-Sample Assuming Equal Variances Input Variable 1 Range: $A$1:$A$12 Variable 2 Range: $B$1:$B$12 OK 1 Cancel 1 Help 0 А B 1 Package A Package B 2 45 56 67 79 4 63 60 5 50 45 6 77 85 7 60 39 8 47 50 9 39 41 10 56 50 11 68 69 12 70 82 13 14 Hypothesized Mean Difference: Labels ck Alpha: 0.05 Output options Output Range: $F$4 1 New Worksheet Ply: New Workbook

Result:

c E F H - t-Test: Two-Sample Assuming Equal Variances Package B 59.64 279.25 11.00 A B 1 Package A Package B 2 45 56 3 67 79 4 63 60 5 50 45 6 77 85 7 60 39 8 47 50 9 39 41 10 56 50 11 68 69 12 70 82 13 14 15 16 17 18 19 20 Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Package A 58.36 143.25 11.00 211.25 0.00 20.00 -0.21 0.42 1.72 0.839 2.09

P-value = 0.839

P-value > α: The differences between the means are not statistically significant

If the p-value is greater than the significance level, you do not have enough evidence to reject the null hypothesis that the population means are all equal.

so it is a false statement. there is no significant difference.