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Quiz 3, Part 2

Quiz 3, Part 2 has two multi-part questions, is untimed (written for about 45 minutes) and is open Stat 311 notes/videos, textbook, and homework/solutions only. You will also be referring to the Problem 2 supplemental handout posted under Quiz 3, Part 2 on Canvas. All responses must be your own. If I suspect    that you collaborated with other people or put down answers that match something you found on the internet, your quiz score will be zero and I will file a report with the Student Conduct office. By uploading your quiz  to Gradescope, you are acknowledging that you adhered to the rules and academic conduct standards set by   the University of Washington.

• Unless specified otherwise, to receive credit you must show your work or give brief explanations, where appropriate.

o You will be graded only on the work you show.

o Partial credit may be given when you show the process used to solve a problem, even if your answer is incorrect.

•   Do not forget units where applicable.

•   Read each problem carefully and follow directions. Make sure you answer the question that is asked.

• Since this quiz is untimed, we expect your solutions to be easy to read! When writing or typing out your solutions, please do not squish all your work together. Leave space between problems and the parts of each problem. If we cannot easily ready your work, it will not be graded. If you upload images, make sure they are dark enough and the angle of the image was such that it is easy to read.

Problem 1 (2 points each): To increase business, the owner of a restaurant is running a promotion in which a customer’s bill can be randomly selected to receive a discount. When a customer’s bill is printed, a program in the cash register randomly determines whether the customer will receive a discount on the bill. The program was written to generate a discount with a probability of 0. 15, that is, giving 15 percent of the    bills a discount in the long run. However, the owner is concerned that the program has a mistake that results  in the program not generating the intended long-run proportion of 0.15. The owner selected a random sample of bills and found that only 10 percent of them received discounts. A confidence interval for p, the proportion of bills that will receive a discount in the long run, is 0.10 ± 0.07. Assume all conditions for inference were met. For this problem, each part is limited to at most two sentences.

a.   Does the confidence interval provide convincing statistical evidence that the program is not working as intended? Answer yes or no and then explain. (0.5 for yes or no; 1.5 for explanation)

b.   Does the confidence interval provide convincing statistical evidence that the program generates the discount with a probability of 0.15? Answer yes, or no and then explain. (0.5 for yes or no; 1.5 for explanation)

Problem 2 (7.5 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 reflect 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, Part 2 on Canvas, we provide a boxplot of  total points by variety, histograms of total points for each coffee variety, with corresponding summary statistics. You are also provided with R output from a two-sample t-test. Use these outputs to answer parts   (a) – (d).

a.   Write down the statistical hypotheses, using symbols, that correspond to the t-test that was run. (2 points)

b.   Using the p-value from the output (and any other numbers you might need), what is your decision with the justification (0.5 points) and conclusion in the context of the problem (1 point) for the hypothesis test that was performed? Use a 10% significance level. Limit of one sentence for decision and one for the conclusion.

c.   Based on your conclusion in part b), what type of statistical error did you risk making? State the error with a justification (0.5 points) and define the error in the context of the problem (1 point). Limit of one sentence for type of error and one sentence for definition in context.

d.   Of the intervals given in the supplementary material, which confidence interval corresponds with the t-test that was performed? Explain your choice of interval (1 point), Report the interval (0.5 points) and

interpret this interval in the context of the problem (1 point). One sentence for each of choice of interval and reporting of interval. At most two sentences for the interpretation of the interval.