A sample of scores for men and women from an examination in Statistics 201 were:

Given that the null hypothesis and the alternative hypothesis
are:
H_{0}: μ_{m} 
μ_{w} ≤ 1
H_{1}: μ_{m}  μ_{w}
> 1
and using a 0.025 significance level conduct a ttest about a difference in population means:
a)  What is the correct decision rule?

b) Compute the pooled variance.
your answer should be accurate to at least four decimal places.
Pooled variance: 0
c) Compute the value of the test statistic.
your answer should be accurate to at least three decimal
places.
Test statistic: 0
d)  What is your decision regarding H_{0}?

Given:
= 0.025
boys:
n1 = 8, = 67.50, S1 = 18.73
girls:
n2 = 9, = 70.78, S2 = 16.22
a)
Degrees of Freedom = n1+n22 = 8 + 9 2 = 15
Critical value:
….....................…Using t table
ANSWER: B
B. Reject Ho in favour of H1 if the computed value of the statistic is greater than 2.131.
b)
Pooled Variance:
pooled Standard deviation = Sp =
C)
Test statistic:
d)
Conclusion:
Test statistic < Critical value, i.e. 0.505 < 2.131, That is Fail to reject Ho at 2.5% level of significance.
ANSWER: C
C. There is insufficient evidence, at the given significance level, to reject H0.
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