MATH 147: Elementary Statistics Fall 2020 Project 2 Instructor: Xiaotian Dai November, 2020 Due Date Submission deadline: Sunday, November 8th, 11:59 pm ET No late submission will be accepted unless a related accomodation request has been granted by the Services for Students with Disabilities. General Description This project assesses your understanding of probability models, statistical sampling, and confidence intervals. You should work individually. Any unauthorized collaboration is prohibited. You should treat this project as a take-home exam. You can seek help for R programming-related problems. You should not consult your TA about statistics-related questions. Submission You need to submit • Your responses to the coding questions. You can submit a .docx or a .pdf file named “Coding.docx” or “Coding.pdf”. • A written response to the short-answer questions. You can print out the questions, write down your solutions, scan the solutions, and submit them in a combined .pdf file named “sa.pdf”. 1-1 1-2 Basic Info & Coding Questions A researcher tried to replicate Mendel’s experiment using a new plant with flowers of three different colors. The colors of the flowers is controlled by a pair of genes with two variants A and a. The rules are: • AA makes red flowers, • Aa and aA make pink flowers, • aa makes white flowers. The parent generation plants only have two different genotypes: AA and aa. Two parent generation plants are crossed (AA × aa) to breed a nunmber of first-generation hybrid plants (F1 generation), and two F1 generation plants are then crossed (Aa × Aa) to produce a number of second-generation hybrid plants (F2 generation). The F2 generation has four different genotypes. For the questions below, show your work and/or R code to receive points. 1. What is your B-number? (2pts) 2. Let x be 100 plus last three digits of your B-number. For example, if last three digits of your B-number is 005, then x = 105. If last three digits of your B-number is 125, then x = 225. You will use this x value for the rest of the project. (1pt) 3. The researcher will breed x number of F2 generation plants. Report the expected value and standard error for the number of plants with red, pink, and white flowers, respectively. You can use R or a calculator to finish this question. (6pts) 4. Create a box model in R representing the colors of plants’ flowers in the F2 generation. Make x draws from the box at random with replacement. For the x number of draws, report the number of red, pink, and white flowers, respectively. (5pts) 1-3 5. Create a box model in R representing the count of plants with pink flowers in the F2 generation. Make 25,000 draws from the box at random with replacement. Save the results in R. Report the percentage of pink flowers in the 25,000 draws, and we will use it as the population percentage. (5pts) 6. Take a simple random sample of 900 plants from the 25,000 plants saved in Question #5. Report the sample percentage for the plants with pink flowers and the 60%-confidence interval for the population percentage. You can use R and/or a calculator to finish this question. When calculating the SD of the box, you can assume that the population percentage is unknown. Make sure you consider the correction factor. (5pts) 7. Repeat the process described in Question #6 four more times. Get four more 60%-confidence intervals for the population percentage. (4pts) 8. For the five confidence intervals obtained in Question #6 and #7, how many intervals cover the population percentage? Explain. (3pts) 1-4 Short-answer questions Use the normal table on page A-104 of your textbook to answer the following questions. Show your work (including the box model used) to receive points. Do not skip steps. 1. The researcher will breed x number of F2 generation plants. (a) What is the probability that more than 26% of the plants will grow red flowers? (5pts) (b) What is the probability that less than 48% of the plants will grow pink flowers? (5pts) 1-5 2. The researcher has decided to cross one parent generation plant (genotype aa) with a F1 generation plant (aa × Aa) in order to breed x number of offspring plants. (a) About what percentage of these plants will grow white flowers? (3pts) (b) What is the probability that more than 48% of these plants will grow white flowers? (5pts) 1-6 3. Suppose that the researcher has bred 25,000 F2 generation plants. He selected a simple random sample of 400 F2 generation plants, and found that 210 plants in the sample have pink flowers. Find the 95%- confidence interval for the percentage of pink flowers in the F2 generation. Interpret the interval. (8pts) 1-7 4. In the sample, the researcher also found that the relationship between the height of a plant and the length of its root can be summarized in the table below: average height ≈ 1.1 ft, SD ≈ 0.2 ft average length of root ≈ 5.5 inches, SD ≈ 0.5 inches, r = xx+100 He is trying to use the height of a plant to predict its length of root. The scatter diagram is football-shaped. (a) Find the regression equation and interpret the coefficients of the equation. (5pts) (b) Of the plants with a height of 1.2 ft, about what percentage have a root of 6 inches or longer? (5pts)
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