Problem 5 (7 points): This problem uses two variables from a coffee data set available on Tidy Tuesday. The main response of interest is coffee tasting that is captured in total points (TotPoints) on a scale from 0 100. The points reect the tastes and aromas of brewed coffee, where a higher score is judged as better. The other variable is variety. For this problem we consider Hawaiian Kona and Yellow Bourbon varieties. In the Quiz 3 supplemental handout that is posted under Quiz 3 on Canvas, we provide a boxplot of total points by variety, histograms of total points for each variety, with corresponding summary statistics. You are also provided with R output from a two-sample r-test. Use these outputs to answer the following questions. a. Write down the statistical hypotheses, using smbols, that correspond to the ttest that was run. (2 points) b. Using the pvalue from the output (and any other numbers you might need), what is your decision and conclusion in the context of the problem for the hypothesis test that was performed? Use a 10% signicance level. (2 points) c. Based on your conclusion in part b), what type of statistical error did you risk making. Briey explain and define the error in the context of the problem. (1 point) d. What is the condence interval that corresponds with the ttest that was performed? Interpret this interval in the context of the problem. (2 points) Quiz 3, Problem 5 Supplementary Materials Hawaiian Kona Yellow Bourbon 15 10 Frequency Frequency 4 6 0 O 75 80 85 78 80 82 84 86 Total Points Total Points Figure 1. Histograms for total points for Hawaiian Kona (left) and Yellow Bourbon (right) varieties. Table 1. Summary statistics for total points for each variety. Variety n Min 01 Median Q3 Max Mean SD Hawaiian Kona 44 72.58 80.31 82.62 83.33 86.25 81.58 3.100 Yellow Bourbon 35 78.00 81.54 82.42 83.17 86.17 82.43 1.578 86 T Total Points 74 78 82 Hawaiian Kona Yellow Bourbon Variety Figure 2. Boxplots showing total points grouped by variety.Various t-test output is shown below. C.HK is a subset with Hawaiian Kona observations and C. YB is a subset with Yellow Bourbon observations. t. test (C. HK$TotPoints, C. YB$TotPoints, alternative = "less") Welch Two Sample t-test data: C. HK$TotPoints and C. YB$TotPoints t = -1. 5824, df = 66. 632, p-value = 0.05915 alternative hypothesis: true difference in means is less than 0 95 percent confidence interval: -Inf 0. 04612384 sample estimates: mean of x mean of y 81 . 57886 82. 43057 # Three confidence intervals calls t. test (C. HK$TotPoints, C. YB$TotPoints, conf . level = 0. 95) $conf.int [1] -1. 9261759 0.2227603 attr (, "conf. level") [1] 0.95 t. test (C. HK$TotPoints, C. YB$TotPoints, conf . level = 0. 90) $conf.int [1] -1. 74953943 0. 04612384 attr (, "conf. level") [1] 0.9 t. test (C. HK$TotPoints, C. YB$TotPoints, conf . level = 0. 80) $conf.int [1] -1. 5484161 -0. 1549995 attr (, "conf. level") [1] 0.8