A researcher tried to replicate Mendels experiment using a new plant with flowers of three different colors.

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Question:

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. Let X= 691

1. 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.

2. 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.

3. 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.

4. Take a simple random sample of 900 plants from the 25,000 plants saved in Question #3. 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.

5. Repeat the process described in Question #4 four more times. Get four more 60%-confidence intervals for the population percentage. 6. For the five confidence intervals obtained in Question #4 and #5, how many intervals cover the population percentage? Explain.