In: Statistics and Probability
For the data below determine if the variances are not equal. Use the six steps of hypothesis testing at a 0.10 level of significance.
x1 = 84, s1 = 10, n = 30
x2 = 85, s2 = 12, n = 25
The corresponding sample variances are:
s12=102=100
s22=122=144
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho:
Ha:
This corresponds to a two-tailed test, for which a F-test for two population variances needs to be used.
(2) Rejection Region
Based on the information provided, the significance level is α=0.10, and the the rejection region for this two-tailed test is R={F:F<0.526 or F>1.945}.
(3) Test Statistics
The provided sample variances are
and
and the sample sizes are given by n1=30 and
n2=25.
The F-statistic is computed as follows:
(4) Decision about the null hypothesis
Since from the sample information we get that FL=0.526<F=0.694<FU=1.945, it is then concluded that the null hypothesis is not rejected.
(5) Conclusion
It is concluded that the null hypothesis Ho is not
rejected. Therefore, there is not enough evidence to claim
that the population variance
is different than the population variance
, at the α=0.10 significance level.
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