Identify the appropriate test statistic or statistics for conducting the following hypothesis tests. (Clearly identify the test statistic and, if applicable, the number of degrees of freedom.
For example, “We conduct the test using an x-statistic with y degrees of freedom.”)
A. H0: μ = 0 versus Ha: μ ≠ 0, where μ is the mean of a normally distributed population with unknown variance. The test is based on a sample of 15 observations.
B. H0: μ = 0 versus Ha: μ ≠ 0, where μ is the mean of a normally distributed population with unknown variance. The test is based on a sample of 40 observations.
C. H0: μ ≤ 0 versus Ha: μ > 0, where μ is the mean of a normally distributed population with known variance σ2. The sample size is 45.
D. H0: σ2 = 200 versus Ha: σ2 ≠ 200, where σ2 is the variance of a normally distributed population. The sample size is 50.
E. H0: σ21 = σ22 versus Ha: σ21 ≠ σ22, where σ21 is the variance of one normally distributed population and σ22 is the variance of a second normally distributed population.
The test is based on two independent random samples.
F. H0: (Population mean 1) − (Population mean 2) = 0 versus Ha: (Population mean 1) − (Population mean 2) ≠ 0, where the samples are drawn from normally distributed populations with unknown variances. The observations in the two samples are correlated.
G. H0: (Population mean 1) − (Population mean 2) = 0 versus Ha: (Population mean 1) − (Population mean 2) ≠ 0, where the samples are drawn from normally distributed populations with unknown but assumed equal variances. The observations in the two samples (of size 25 and 30, respectively) are independent.
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