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A lab assignment for econ 230 students to understand and calculate simple probabilities and conditional probabilities using the multiplication rule and addition rule. Students are required to create a table with qualitative and quantitative variables, find probabilities of being in specific rows and columns, and use the multiplication rule and addition rule to find probabilities of combinations of events.
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Lab 3 The goal of this lab is to understand and find simple probabilities and conditional probabilities, and to use the Multiplication Rule and the Addition Rule. Part 1: Create a table with your qualitative variable V 1 and quantitative variable V 2****. (2 points) For your Qualitative Variable, return to Lab 2 and choose the largest slice of the pie graph to label the first column. Label the second column “others”. For your Quantitative Variable, V 2 , label the first row LOW to indicate values that are at “the median or lower.” Label the second row as HIGH to indicate values that are “higher than the median.” You found the median in Lab 2. For a student who has more high literacy countries than any other type, the chart will look like: Qualitative Variable, V 1 (literacy) Quantitative Variable, V 2 (Life expectancy) For the data in the chart, this student has 22 high literacy countries, 9 of which have low values for life expectancy and 13 of which have high values for life expectancy. This student has 18 countries which are not high literacy, 10 of which have low values for life expectancy and 8 of which have high values for life expectancy. If there is a tie between high and low literacy for the most common category, choose high as the most common category. If there is a tie between high and medium literacy for the most common category, choose high as the most common category. If there is a tie between medium and low literacy for the most common category, choose medium as the most common category. Look at your data and count up the observations for each of the four cells in the table. Place the sums in each cell and be sure that the numbers in all of the cells sum to 40. Also record the sums for each row and each column. Part 2: Find simple probabilities. (1 point each) A. Compute the probability of being in Row 1. (For example, P(low value for life expectancy) ). B. Compute the probability of being in Column 1. (For example, P(high literacy) ). High Others Low 9 10 High 13 8
C. Compute the probability of being in Row 1 and Column 1 using the appropriate frequency from your table. (For example, P(high literacy and low life expectancy )). Part 3: Find conditional probabilities. (1 point) Find the probability of being in Row 1, given Column 1. (For example, P(low value for life expectancy, given high literacy) ). Part 4: Multiplication Rule (2 points) If you choose two countries from your sample, use the Multiplication Rule to find the probability that they are both from Column 1. (For example, P(both countries have high literacy) ). Hint: You will be sampling without replacement. Part 5: Addition Rule (1 point each) A. Use the Addition Rule to find the probability of being in Row 1 or Column 1. B. Use the Addition Rule to find the probability of being in Row 1 or Row 2.
Answer: _____________________ Part 3: Answer: _____________________ Part 4: Answer: _____________________
Part 5 A. Answer: _____________________ B. Answer: _____________________