2. An experiment involving 150 individuals randomly assigned each individual to receive a particular treatment for a urinary tract infection (UTI) and whether or not each individual's UTI was resolved (i.e. cured) after a certain treatment periodEI The data is summarized in the following table: Control Cranberry Juice Lactobacillus UTI resolved 32 42 30 UTI unresolved 18 8 20 The interest is in determining if there is an association between treatment type and UTI status, using a Chi-square Test. (a) Clearly state the appropriate null and alternative hypotheses under investigation (b) Create a second table that is the same dimensions as the one above, in which the expected values for each cell have been calculated. You do NOT need to show your calculations for each expected value, just including the second table is sufcient. (c) Calculate the test statistic and obtain a p-value. You do NOT need to show every step of your calculations for your test statistic. (d) What conclusion can you make regarding the association between treatment type and UTI status? (e) Verify your results using the function chisq.test in R. Include your output from the test in your solutions. 0 Hint #1: Use ?chisq.test to open the help le for this function. You do NOT want to apply the continuity correction. o Hint #2: It is helpful to enter your data into R using the matrix function. Always remember to view your data so you can see if you set it up correctly. (f) This study was conducted as a designed experiment, which allowed the researchers to control for potential confounding variables. Identify one potential confounding variable that could have inuenced the results, and explain how / why it is a potential confounding variable using a confounding diagram to illustrate your argument. How do you suppose the researchers controlled for this confounding variable