5. Good news: after you performed your analyses in problem \#4, your research assistant now tells you the piece of paper with the stream labels for the rocks has been found, so that the rocks from the riffles and the pools can be identified with each stream [see dataset \#5]. We'd like to know whether mean algal AFDM differs between pools and riffles. (3 pts) (a) Determine the mean difference in algal biomass between habitats and the 95% confidence interval for the mean difference. (1 pt) (b) Verify that the differences are normally distributed by performing a Shapiro-Wilk test. Report both the W and P. (2 pts) (c) State (be specific!) your null and altemative hypotheses for this revised dataset that has labeled streams. (8 pts) (d) Perform the most appropriate test of your hypotheses in (c) and report your result and state your conclusions. Be sure to indicate: - statistical test performed - value of test statistic (and degrees of freedom if applicable) - P-value - conclusion (4 pts) (e) Compare your answers for part (d) for this problem with part (e) from 44 and explain. Even though the data numbers are identical, why are the results dramatically different? What is the general term for the handling of the data in this problem? What problems of experimental design does this address? \begin{tabular}{lcc} & Riffles: Algal ADFM (m2) & Pools: Algal ADFM (gm2) \\ \hline Mill Run & 111 & 111 \\ Wolf Run & 87 & 92 \\ Little Sugar Creek & 108 & 110 \\ Britton Run & 105 & 106 \\ Cussewago Creek & 122 & 128 \\ Woodcock Creek & 157 & 148 \\ Muddy Creek & 99 & 106 \\ Mohawk Run & 134 & 144 \\ Carr Run & 113 & 116 \\ Conneaut Creek & 132 & 139 \\ Cemetery Run & 135 & 134 \\ Gravel Run & 98 & 108 \\ Bossard Run & 140 & 154 \\ Price Road Run & 147 & 156 \\ Conneauttee Creek & 150 & 169 \\ Inlet Run & 114 & 118 \\ MicMichael Run & 139 & 151 \\ Conneaut Outlet & 122 & 130 \\ Deckard Run & 116 & 122 \\ Federal Run & 102 & 103 \\ \hline \end{tabular}