Consider the Two Data Sets Shown ACalculate the Difference in Means Between the Two Data Sets

Essay

Consider the two data sets shown. Imagine that we are interested if the mean of the second population is larger than the mean of the first population and we wish to test this using the bootstrap procedure. We will use a one-tailed approach with the alternative hypothesis being a situation in which the mean of the second population exceeds the first.
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$\begin{array}{c}{\text { Samples }} \\\begin{array}{|ll|}\hline A & \text { B } \\ 5 & 9 \\6 & 8 \\8 & 7 \\4 & 5 \\7 & 9 \\3 & 8 \\9 & 5 \\1 & 5 \\5 & 7 \\2 & 8 \\\hline\end{array}\end{array}$
a.Calculate the difference in means between the two data sets. Is this consistent with the null hypothesis or the alternative hypothesis?
b.Perform a single bootstrap and calculate the difference between the means of the two groups. Use the first set of digits from π below as a method to generate the appropriate random numbers for each group (treat zeroes as a 10) and then sequentially choose the appropriate number of bootstrap values from each sample, starting with the first sample. Clearly show which values you use and how (i.e., show your work).
c.Is the difference in means from part (b) consistent with the null or alternative hypothesis?
d.What would our conclusion be if we performed 99 more replicates and they showed the same general pattern (i.e., the sign of the difference) as in part (c)?
π = 31415926535897932384626433