Please answer the following questions using STAT:

Tea, Coffee, and Your Immune System Researchers suspect that drinking tea might enhance the production of interferon gamma, a molecule that helps the immune system fight bacteria, viruses, and tumors. A recent study' involved 21 healthy people who did not normally drink tea or coffee. Eleven of the participants were randomly assigned to drink five or six cups of tea a day, while 10 were asked to drink the same amount of coffee. After two weeks, blood samples were exposed to an antigen and production of interferon gamma was measured." The results are shown in Table 1 and are available in ImmuneTea. We are interested in estimating the effect size, the increase in average interferon gamma production for drinking tea when compared to coffee. Tea 5 11 13 18 20 47 48 52 55 56 58 Coffee 0 3 11 15 16 21 21 38 52 Table 1 Immune system response in ted and coffee drinkers Click here for the dataset associated with this question. Click here to access StotKey. (e) Use Stotkey or other technology to estimate the difference in mean production for tea drinkers minus coffee drinkers. Round your answer to two decimal places. $ 1 - X. = 1 [b) Give the standard error for the difference. Round your answer to one decimal place. standard error = 1 (c) Give a 95 % confidence interval. Round your answers to two decimal places. The 95 % confidence interval is a to Adapted from Kamath et.al., "Antigens in tea-Beverage Prime Human Vy2V62 T Cells in vitro and in vivo for Memory and Non-memory Antibacterial Cytokinesponses." Proceedings of the National Academy of Sciences, May 13, 2003. "To be specific, peripheral blood mononuclear cells were cultured with the antigen alkylamine ethylalamine in an enzyme linked immunospot assay to the frequency of interferon-gamma-producing cells.NHL Penalty Minutes Table 1 shows the number of points scored and penalty minutes for 26 ice hockey players on the Ottawa Senators NHL team for the 2018-2019 season. The data are also stored in OttawaSenators2019. Assume that we consider these players to be a sample of all NHL players. Points 48 19 42 22 26 45 41 35 55 28 10 62 44 Pen mins 26 35 18 75 24 81 27 22 29 Points 15 5 5 58 12 2 14 12 14 14 Pen mins 20 89 56 14 2 10 6 O 4 Table 1 Points and penalty minutes for the 2014-2015 Ottawa Senators NHL team Click here for the dataset associated with this question. Click here to access Stotkey. (a) You are given a dotplot of the distribution of penalty minutes (PenMin) for the original sample of 26 players. 12 24 36 48 60 72 B4 PenMins Comment on the shape, paying particular attention to skewness and possible outliers. The sample is The outlier(s) is/are minutes. eTextbook and Media (b) Find the mean and standard deviation of the penalty minute values for the original sample. Round to two decimal places. Mean = minutes Standard deviation = 1 minutes eTextbook and Media(c) You are given a bootstrap distribution for the mean penalty minutes for samples of size n = 26 NHL players. Bootstrap Dotplot of Mess . 150 left The Tae-Tall Right Toll 125 100 75 50 10 15 20 25 45 4.45 Comment on the shape of this distribution. O The distribution is left-skewed and centered near 17.05. O The distribution is faily symmetric and centered near 24.5. O The distribution is right-skewed and centered near 4.8. eTextbook and Media [d) Compute the standard deviation of the bootstrap means using the distribution in part (c). Round to two decimal places. i eTextbook and Media (e) Construct a 95% confidence interval for the mean penalty minutes of NHL players. Round to two decimal places. i to minutes