1. Many coffee drinkers say that they experience an increase in heart rate after consuming a cup of coffee. A sample of 4 people had their resting heart rate measured, were given 300 ml of coffee to drink, and then ten minutes later had their heart rate measured again. The data from these samples is given in the chart below. Perform a paired-samples t-test, with a p level of 0.05 to determine if the persons mean Heart Rate Heart Rate heart rate does increase after ingesting coffee. Before (X) After [Y) [bom] [bom a) If Population 1 is defined as the heart rates after ingesting coffee and Population 2 is 82 87 defined as the heart rates before ingesting coffee, define a, and #2. [1] 66 71 78 86 b) State the null and alternative hypothesis, and if this is two-tailed, right-tailed, or left tailed test [2] 97 c) Use the following table to help determine the mean of the difference scores (d ) and the standard deviation: X Y D = Y-X D-d (D - d) [5] d) Find tos , that is find the cut-off(s) for a p level of 0.05 [1] e) Find the value of the t-test statistic(s), and show it in a diagram relative to tos [2]f) Conclude on your findings, both generally and specifically to this problem [2] g) Using the information from the sample of 4 people, give the 90%% confidence interval for the population mean difference in heart rate. (3] 2. Consider the following data: X 6.4 2.6 7.1 4.5 Y 3.3 6.7 3.7 5.3 6.1 4.6 Use the steps below to determine the value of Spresence. (Note: you are not performing the hypothesis test, just finding this one value) a) Find the value of the following: [2] b) It will be helpful to know that s = 4.097 and s/ = 1.783. Now find the following: [4] dfx = Nx - 1= d ftotal = dfx + dfy = dfy = Ny - 1= Spooked = c) Determine: [2] Nx NY d) Determine: [1] Sairference = Sky + Sky =difference e) Finally, determine: [1] Sayfema = 3. A new drug is being tested to relieve nausea symptoms in cancer patients who are undergoing chemotherapy treatment. Over a 6 week period, a sample of 12 patients were studied each taking the same amount of the drug at the same intervals. The patients weighed themselves each week and recorded their mean weight, and also noted the amount of time that they experienced relief after taking the drug, and recorded that as well. The results are listed below. Mean Weight 204.2 121.2 142.9 154.8 129.7 164.1 135.4 124.6 176.2 188.3 145.7 173.3 [Ibs) Mean Y Relief Time 3.9 6.6 4.3 5.6 8.7 9.9 4.6 3.5 7.4 6.2 [hrs) a) Type the data into Excel and use the Excel functions listed to determine the value of each of the following. Note: The first two functions must have the range of y-values listed first. [2] Excel Function Value Slop of the least squares line (b) =SLOPE (#:#) Intercept of the least squares line (a) =INTERCEPT(# #) Correlation coefficient (r) =CORRELA:#) Coefficient of determination (r= ) =CORREL(# #)42 b) A correlation coefficient is considered strong if 0.7 s |r|