2 Sample Hypothesis test ?

Question

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

(a) State the hypothesis for a right-tailed test

(b) Obtain a test statistic and p-value assuming equal variances. Interpret these results.

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

(d) Is it reasonable to assume equal variances?

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

Answer 1

TESTS BETWEEN TWO MEANS, POOLED T-TEST

[Normal populations or n1 + n2 > 40) and independent observations and σ1 = σ2 and (σ1 and σ2 unknown)]

(a) Null hypothesis: H0 μ1 - μ2 = 0, Alternative hypothesis: Ha μ1 - μ2 > 0 ("right-tailed" test requirement)

(b) Test Statistic formulae:

http://en.wikipedia.org/wiki/Statistical...

Two-sample pooled t-test

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean

1 25 77.1 19.6 3.9

2 24 69.3 24.9 5.1

Difference = mu (1) - mu (2)

Estimate for difference: 7.80000

95% lower bound for difference: -2.91757

T-Test of difference = 0 (vs >): T-Value = 1.22 P-Value = 0.114 DF = 47

Both use Pooled StDev = 22.3512

(c) P-Value > α [ 0.114 > 0.05]. Cannot reject Null Hypothesis H0 μ1 - μ2 = 0. There is not a significant difference between FIRST and LATER.

(d) Yes! It is reasonable to assume equal variances. Samples are from same population.