Statistics - Two Sample t-test with Known and Unequal Variances

Running Head: STATISTICS
Statistics
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1STATISTICS
Table of Contents
Answers:..........................................................................................................................................2
Answer 1......................................................................................................................................2
Part A........................................................................................................................................2
Part B........................................................................................................................................4
References:......................................................................................................................................5

2STATISTICS
Answers:
Answer 1.
Part A
Assumptions:
The t-test for two population means corresponds a right-tailed tests. The two samples are needed
to be independent with each other (Boneau 1960).
Provided description:
The given problem indicates that the mean ( X 1) = 82 and (X 2) = 81. On the other hand,
standard deviations of two samples are- S1= 6 and S2= 4. The sample sizes of two different data
sets are- n1= 252 and n2= 150.
Test applied:
Two sample t-test with known and unequal variances. The t-test is one-tailed.
Hypotheses:
Null hypothesis (H0): The averages of scores of male and female students are equal to each other
(μ1= μ2).
Alternative hypothesis (H0): The average score of female students is greater than the average
score of male students (μ1> μ2).
Region of rejection:
On the basis of provided information, the significance level is assumed to be α= 5%.
The rejection region for this right-tailed test is R = {α: α<0.05} = {t: t>tcrit}.
Test statistic:
The t-statistic of population variances is computed as-