Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices. So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles. Indicate which of the following is the null hypothesis, and which is the alternate hypothesis. There food preferences among vole species are independent of one another. There is a relationship between voles and food preference. To test for independence, we need to calculate the Chi-square statistic. These are the data that Dr. Pagels collected: meadow voles common voles 19 28 apple slices peanut butter-oatmeal 17 27 • You will want to use Excel (or Google sheets) to do the calculations for you, so that your answers are exact (they need to be exact to get credit. Here is a Google sheet to get you started. • When transferring your answers, make sure you carry them out to AT LEAST SIX SIGNIFICANT FIGURES unless otherwise stated. Round your final answer to 4 decimal places expected meadow vole/apple slices %3D = expected common vole/apple slices expected meadow vole/peanut butter-oatmeal %3D expected common vole/peanut butter-oatmeal = chi-square value degrees of freedom (whole number only) = using Statistical Table A (pg 704 of your textbook), what is the chi-square critical value with significance level of X=0.05? (report exactly the value in the table) = will you reject or fail to reject the null hypothesis? (answer either reject or fail to reject)