Q1) To test hypothesis that students who finish exam first get better grades, Professor Hardtack kept track of order in which papers were handed in. First 25 papers showed a mean score of 77.1 with standard deviation of 19.6, while last 24 papers handed in showed mean score of 69.3 with standard deviation of 24.9. Is this significant difference at α = .05?    

a) State the hypotheses for a right-tailed test.

b) Get a test statistic and p-value suppose equal variances.Interpret these results.

c) Is difference in mean scores large enough to be important?

d) Is it sensible to assume equal variances?

e) Carry out a formal test for equal variances at α = .05, showing all steps clearly.