# 1. Return to the US News dataset on Tier I National Universities. ...

## Question

1. Return to the US News dataset on Tier I National Universities.
2. Perform a t test the difference in mean PeerRating, HSGCRating, GradRate and AlumSalary between public and private schools using a .05 level of significance.
3. Perform an ANOVA test of the differences in mean PeerRating and HSGCRating by levels of Selectivity using a .05 level of significance.
4. For the crosstabulation of Selectivity by Type and Region by Type, test the differences between types using chi-square with a .05 level of significance
5. Write a report (in MS Word) describing and interpreting the results of your analyses, inserting the any charts and tables where they belong.

## Solution Preview

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Excel Output:
F-Test Two-Sample for Variances

Private PeerRating, Public PeerRating
Mean 3.152040816 3.223469388
Variance 0.794274143 0.229237324
Observations 98 98
df 97 97
F 3.46485524
P(F<=f) one-tail 1.5785E-09
F Critical one-tail 1.398866187

t-Test: Two-Sample Assuming Unequal Variances

Private PeerRating, Public PeerRating
Mean 3.152040816 3.223469388
Variance 0.794274143 0.229237324
Observations 98 98
Hypothesized Mean Difference 0
df 149
t Stat -0.698937989
P(T<=t) one-tail 0.242840174
t Critical one-tail 1.655144534
P(T<=t) two-tail 0.485680347
t Critical two-tail 1.976013145

Interpretation:
From the above output, we can see that the variance of Peer Assessment Rating (PeerRating) is not equal between public and private schools because the F-Test Two-Sample for Variances has p-value 0.0000 which is smaller than 0.05 so we will use “t-Test: Two-Sample Assuming Unequal Variances”. The t test output gives the two sided p-value as 0.4856 which is bigger than 0.05, so we can conclude that there is no statistically significant difference in mean Peer Assessment Rating between public and private schools....

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