Question: Two-sample t-procedures for comparing means – generic problem (CH 12):

A researcher is interested in comparing the means of two populations. The hypothesis of interest is the hypothesis of "no difference" – that the two means are equal to each other and therefore the difference is zero: \({{\mu }_{1}}-{{\mu }_{2}}=0\).

The researcher collects independent random samples of data from each population:

1. Perform a two-sample t-test to test the null hypothesis of "no difference" against the two-sided alternative hypothesis:
   \[\begin{aligned} & {{H}_{0}}:{{\mu }_{1}}-{{\mu }_{2}}=0 \\ & {{H}_{A}}:{{\mu }_{1}}-{{\mu }_{2}}\ne 0 \\ \end{aligned}\]
   To save you some time, the data is available in the HW4 data.xls Excel file that is posted separately to BlazeView. Assume that the data comes from normally distributed populations. Use statistical software to calculate the appropriate degrees of freedom, test statistic, and p-value. What is the appropriate conclusion to this hypothesis test?
2. The means of the two samples of data are not equal to each other – this is a fact. Are the two means close enough in value that the difference could be due to chance rather than a true difference in the means of the underlying populations?

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