I attached the data set and the homework assignment.
Directions: Write your R codes, in addition to your answer, to the following 10 problems. Include any relevant figures and plots in your solution. Data: The data set Tips, a .csv file, contains data on tipping behavior collected by one waiter. See https://vincentarelbundock.github.io/Rdatasets/doc/reshape2/tips.html for more information. Note: Throughout this paper I refer to the cases in the data set as a “party”. 1. For each variable, identify its data type (e.g. categorical, discrete). 2. (Find the following values. a. The total bill of the 88th party b. The size of parties 153-159 c. The minimum tip among non-smokers. 3. Using at least 2 methods, determine if total_bill follows a normal distribution. Justify your answers. 4. Consider the variables: tip and total_bill. Assume that total_bill represents the cost of the food, before the tip is added. a. Which variable is the explanatory variable? b. Describe the relationship between the variables. Justify your answer with a plot and be sure to discuss any unusual observations. 5. Using numerical summaries and a side-by-side boxplot, determine if there is a relationship between the time during which people dine and how they tip. 6. (Let equal the size of a randomly selected Dinner party. a. Find the probability distribution for . b. Find the expected value of . c. Find the standard deviation of . 7. Find the probability that a randomly selected party a. dined on Friday or is a smoker. b. gave a tip that was less than 15% of the total bill. 8. Find the conditional probability that a. the size of the party was greater than 3 given that the day they dined was Saturday. b. they tipped more than $5 given that the size of the party was less than 3. 9. Is being a smoker independent of one’s sex? Justify your answer using the data. 10. Let equal the number of smokers for a random sample of 5 parties. a. Use the binomial distribution to approximate the probability that . b. Could we use the normal distribution to approximate the answer in part a? Justify your answer. (continued on back) total_bill,tip,sex,smoker,day,time,size 16.99,1.01,Female,No,Sun,Dinner,2 10.34,1.66,Male,No,Sun,Dinner,3 21.01,3.5,Male,No,Sun,Dinner,3 23.68,3.31,Male,No,Sun,Dinner,2 24.59,3.61,Female,No,Sun,Dinner,4 25.29,4.71,Male,No,Sun,Dinner,4 8.77,2,Male,No,Sun,Dinner,2 26.88,3.12,Male,No,Sun,Dinner,4 15.04,1.96,Male,No,Sun,Dinner,2 14.78,3.23,Male,No,Sun,Dinner,2 10.27,1.71,Male,No,Sun,Dinner,2 35.26,5,Female,No,Sun,Dinner,4 15.42,1.57,Male,No,Sun,Dinner,2 18.43,3,Male,No,Sun,Dinner,4 14.83,3.02,Female,No,Sun,Dinner,2 21.58,3.92,Male,No,Sun,Dinner,2 10.33,1.67,Female,No,Sun,Dinner,3 16.29,3.71,Male,No,Sun,Dinner,3 16.97,3.5,Female,No,Sun,Dinner,3 20.65,3.35,Male,No,Sat,Dinner,3 17.92,4.08,Male,No,Sat,Dinner,2 20.29,2.75,Female,No,Sat,Dinner,2 15.77,2.23,Female,No,Sat,Dinner,2 39.42,7.58,Male,No,Sat,Dinner,4 19.82,3.18,Male,No,Sat,Dinner,2 17.81,2.34,Male,No,Sat,Dinner,4 13.37,2,Male,No,Sat,Dinner,2 12.69,2,Male,No,Sat,Dinner,2 21.7,4.3,Male,No,Sat,Dinner,2 19.65,3,Female,No,Sat,Dinner,2 9.55,1.45,Male,No,Sat,Dinner,2 18.35,2.5,Male,No,Sat,Dinner,4 15.06,3,Female,No,Sat,Dinner,2 20.69,2.45,Female,No,Sat,Dinner,4 17.78,3.27,Male,No,Sat,Dinner,2 24.06,3.6,Male,No,Sat,Dinner,3 16.31,2,Male,No,Sat,Dinner,3 16.93,3.07,Female,No,Sat,Dinner,3 18.69,2.31,Male,No,Sat,Dinner,3 31.27,5,Male,No,Sat,Dinner,3 16.04,2.24,Male,No,Sat,Dinner,3 17.46,2.54,Male,No,Sun,Dinner,2 13.94,3.06,Male,No,Sun,Dinner,2 9.68,1.32,Male,No,Sun,Dinner,2 30.4,5.6,Male,No,Sun,Dinner,4 18.29,3,Male,No,Sun,Dinner,2 22.23,5,Male,No,Sun,Dinner,2 32.4,6,Male,No,Sun,Dinner,4 28.55,2.05,Male,No,Sun,Dinner,3 18.04,3,Male,No,Sun,Dinner,2 12.54,2.5,Male,No,Sun,Dinner,2 10.29,2.6,Female,No,Sun,Dinner,2 34.81,5.2,Female,No,Sun,Dinner,4 9.94,1.56,Male,No,Sun,Dinner,2 25.56,4.34,Male,No,Sun,Dinner,4 19.49,3.51,Male,No,Sun,Dinner,2 38.01,3,Male,Yes,Sat,Dinner,4 26.41,1.5,Female,No,Sat,Dinner,2 11.24,1.76,Male,Yes,Sat,Dinner,2 48.27,6.73,Male,No,Sat,Dinner,4 20.29,3.21,Male,Yes,Sat,Dinner,2 13.81,2,Male,Yes,Sat,Dinner,2 11.02,1.98,Male,Yes,Sat,Dinner,2 18.29,3.76,Male,Yes,Sat,Dinner,4 17.59,2.64,Male,No,Sat,Dinner,3 20.08,3.15,Male,No,Sat,Dinner,3 16.45,2.47,Female,No,Sat,Dinner,2 3.07,1,Female,Yes,Sat,Dinner,1 20.23,2.01,Male,No,Sat,Dinner,2 15.01,2.09,Male,Yes,Sat,Dinner,2 12.02,1.97,Male,No,Sat,Dinner,2 17.07,3,Female,No,Sat,Dinner,3 26.86,3.14,Female,Yes,Sat,Dinner,2 25.28,5,Female,Yes,Sat,Dinner,2 14.73,2.2,Female,No,Sat,Dinner,2 10.51,1.25,Male,No,Sat,Dinner,2 17.92,3.08,Male,Yes,Sat,Dinner,2 27.2,4,Male,No,Thur,Lunch,4 22.76,3,Male,No,Thur,Lunch,2 17.29,2.71,Male,No,Thur,Lunch,2 19.44,3,Male,Yes,Thur,Lunch,2 16.66,3.4,Male,No,Thur,Lunch,2 10.07,1.83,Female,No,Thur,Lunch,1 32.68,5,Male,Yes,Thur,Lunch,2 15.98,2.03,Male,No,Thur,Lunch,2 34.83,5.17,Female,No,Thur,Lunch,4 13.03,2,Male,No,Thur,Lunch,2 18.28,4,Male,No,Thur,Lunch,2 24.71,5.85,Male,No,Thur,Lunch,2 21.16,3,Male,No,Thur,Lunch,2 28.97,3,Male,Yes,Fri,Dinner,2 22.49,3.5,Male,No,Fri,Dinner,2 5.75,1,Female,Yes,Fri,Dinner,2 16.32,4.3,Female,Yes,Fri,Dinner,2 22.75,3.25,Female,No,Fri,Dinner,2 40.17,4.73,Male,Yes,Fri,Dinner,4 27.28,4,Male,Yes,Fri,Dinner,2 12.03,1.5,Male,Yes,Fri,Dinner,2 21.01,3,Male,Yes,Fri,Dinner,2 12.46,1.5,Male,No,Fri,Dinner,2 11.35,2.5,Female,Yes,Fri,Dinner,2 15.38,3,Female,Yes,Fri,Dinner,2 44.3,2.5,Female,Yes,Sat,Dinner,3 22.42,3.48,Female,Yes,Sat,Dinner,2 20.92,4.08,Female,No,Sat,Dinner,2 15.36,1.64,Male,Yes,Sat,Dinner,2 20.49,4.06,Male,Yes,Sat,Dinner,2 25.21,4.29,Male,Yes,Sat,Dinner,2 18.24,3.76,Male,No,Sat,Dinner,2 14.31,4,Female,Yes,Sat,Dinner,2 14,3,Male,No,Sat,Dinner,2 7.25,1,Female,No,Sat,Dinner,1 38.07,4,Male,No,Sun,Dinner,3 23.95,2.55,Male,No,Sun,Dinner,2 25.71,4,Female,No,Sun,Dinner,3 17.31,3.5,Female,No,Sun,Dinner,2 29.93,5.07,Male,No,Sun,Dinner,4 10.65,1.5,Female,No,Thur,Lunch,2 12.43,1.8,Female,No,Thur,Lunch,2 24.08,2.92,Female,No,Thur,Lunch,4 11.69,2.31,Male,No,Thur,Lunch,2 13.42,1.68,Female,No,Thur,Lunch,2 14.26,2.5,Male,No,Thur,Lunch,2 15.95,2,Male,No,Thur,Lunch,2 12.48,2.52,Female,No,Thur,Lunch,2 29.8,4.2,Female,No,Thur,Lunch,6 8.52,1.48,Male,No,Thur,Lunch,2 14.52,2,Female,No,Thur,Lunch,2 11.38,2,Female,No,Thur,Lunch,2 22.82,2.18,Male,No,Thur,Lunch,3 19.08,1.5,Male,No,Thur,Lunch,2 20.27,2.83,Female,No,Thur,Lunch,2 11.17,1.5,Female,No,Thur,Lunch,2 12.26,2,Female,No,Thur,Lunch,2 18.26,3.25,Female,No,Thur,Lunch,2 8.51,1.25,Female,No,Thur,Lunch,2 10.33,2,Female,No,Thur,Lunch,2 14.15,2,Female,No,Thur,Lunch,2 16,2,Male,Yes,Thur,Lunch,2 13.16,2.75,Female,No,Thur,Lunch,2 17.47,3.5,Female,No,Thur,Lunch,2 34.3,6.7,Male,No,Thur,Lunch,6 41.19,5,Male,No,Thur,Lunch,5 27.05,5,Female,No,Thur,Lunch,6 16.43,2.3,Female,No,Thur,Lunch,2 8.35,1.5,Female,No,Thur,Lunch,2 18.64,1.36,Female,No,Thur,Lunch,3 11.87,1.63,Female,No,Thur,Lunch,2 9.78,1.73,Male,No,Thur,Lunch,2 7.51,2,Male,No,Thur,Lunch,2 14.07,2.5,Male,No,Sun,Dinner,2 13.13,2,Male,No,Sun,Dinner,2 17.26,2.74,Male,No,Sun,Dinner,3 24.55,2,Male,No,Sun,Dinner,4 19.77,2,Male,No,Sun,Dinner,4 29.85,5.14,Female,No,Sun,Dinner,5 48.17,5,Male,No,Sun,Dinner,6 25,3.75,Female,No,Sun,Dinner,4 13.39,2.61,Female,No,Sun,Dinner,2 16.49,2,Male,No,Sun,Dinner,4 21.5,3.5,Male,No,Sun,Dinner,4 12.66,2.5,Male,No,Sun,Dinner,2 16.21,2,Female,No,Sun,Dinner,3 13.81,2,Male,No,Sun,Dinner,2 17.51,3,Female,Yes,Sun,Dinner,2 24.52,3.48,Male,No,Sun,Dinner,3 20.76,2.24,Male,No,Sun,Dinner,2 31.71,4.5,Male,No,Sun,Dinner,4 10.59,1.61,Female,Yes,Sat,Dinner,2 10.63,2,Female,Yes,Sat,Dinner,2 50.81,10,Male,Yes,Sat,Dinner,3 15.81,3.16,Male,Yes,Sat,Dinner,2 7.25,5.15,Male,Yes,Sun,Dinner,2 31.85,3.18,Male,Yes,Sun,Dinner,2 16.82,4,Male,Yes,Sun,Dinner,2 32.9,3.11,Male,Yes,Sun,Dinner,2 17.89,2,Male,Yes,Sun,Dinner,2 14.48,2,Male,Yes,Sun,Dinner,2 9.6,4,Female,Yes,Sun,Dinner,2 34.63,3.55,Male,Yes,Sun