10 DIRECTIONS In a typed word processing document, clearly answer the following questions. Be sure to show all of your work by providing your R commands, solutions/output, and interpretation. For the following questions, determine whether to use a parametric or non-parametric test (look at assumptions or test for normality). Perform the hypothesis testing in R and write down the results and the R commands you used. Draw the distribution with the critical values. Where needed perform tests at =0.05. Make conclusions using both the p-value and test statistic. Underline your answers. A) The zika virus has been linked to severe neurological diseases and can cause microcephaly, reducing the brain size of a baby. Ultrasounds have measured the brain size (cm) of 3-week-old babies in the womb before and after infection of zika Before zika: 12.9, 13.5, 12.8, 15.6, 17.2, 19.2, 12.6, 15.3, 14.4, 11.3 After zika: 12.7, 11.6, 10, 15.2, 16.8, 20, 12, 15.5, 15, 10.9 - First state the null and alternative hypothesis. -Test for the normality of the distributions. Are the samples normally distributed? - Is there a decrease in brain size after zika infection (assume the data is normally distributed)? B) You are asked to test whether pollution levels in a nearby pond are reduced by stopping industrial waste dumping. Here the values of pollution at each site: With dumping (before): 214, 159, 169, 272, 103, 179, 200, 149, 132, 148, 194, 104, 219, 119, 234 Without dumping (after): 159, 135, 141, 101, 102, 168, 62, 167, 174, 159, 66, 118, 181, 171, 112 -First state the null and alternative hypothesis. -Does stopping waste dumping decrease levels of pollution in the pond assume the data is normally distributed)? -Plot both the With dumping and Without dumping values in different colors and symbols on the same plot. Label both axes. C) 6 subjects were given a drug to dull pain. Their reaction time to a shock stimulus was measured (in ms). Prior to treatment: 91, 87, 99, 77, 81, 91, 75 After Treatment: 91, 99, 103, 111, 99, 104, 102 -First state the null and alternative hypothesis. -Did the drug increase the resistance to pain (assume the data is normally distributed)? D) You are asked to compare the average wing size (in cm) of two groups of Drosophila melanogaster. The first group consists of Drosophila from brazil; the second group is North America Drosophila. The data are given below. Brazilian = 18, 22, 21, 17, 20, 17, 23, 20, 22 ,21 North America = 16, 17, 14, 21, 19, 18, 13, 15, 17, 21 -First state the null and alternative hypothesis. -Is the wing size equal in both groups (assume the data is normally distributed and the variances are equal)