1. The weight of a potato sold at a grocery store is normally distributed with a mean of 375 grams and a standard deviation of 50 grams. A. You picked a potato at random. What is the probability that the weight is between 300 and 400 grams? B. You took a sample of 9 potatoes. What is the probability that the average weight of a potato in this sample lies between 300 and 400 grams? 2. The weight of a potato sold at New Grocers grocery store is normally distributed with a mean of 375 grams and a standard deviation of 75 grams. They have a store in an affluent neighborhood where they remove potatoes that do not look fresh and charge a higher price. You believe that the average weight of a potato at this store is higher than 375 grams. You took a sample of 9 potatoes and the weight is 350 grams. What is your conclusion? Use =.05. 3. You started a new supplier and believe that the average weight of a potato from the supplier is different from 375 grams. To test your hypothesis, you took a sample of 16 potatoes. The average weight of a potato in this sample is 355 grams and the standard deviation is 24 grams. What is your conclusion? Use =.05. 4. You are given data on happiness level, perceived corruption, and social cohesion. Run a regression of happiness level on the other two variables and interpret the results, i.e., interpret R2, F-test and t-test results in the regression output that you obtain. H/L P/C S/C 7.350 81.00 1.40 7.369 69.00 1.30 6.967 75.00 1.30 7.477 81.00 1.30 6.587 71.00 1.60 6.290 48.00 1.40 7.693 91.00 1.20 5.426 68.00 1.70 7.389 89.00 1.30 6.764 71.00 1.90 6.672 78.00 1.40 5.435 40.00 2.00 4.775 54.00 1.50 7.355 78.00 1.20 7.076 72.00 1.40 7.301 61.00 2.70 6.021 43.00 1.70 6.064 74.00 1.30 6.267 55.00 1.80 7.054 80.00 1.30 7.088 34.00 2.40 7.512 83.00 1.50 7.221 91.00 1.20 7.655 86.00 1.40 5.822 60.00 1.50 5.101 62.00 1.50 5.969 47.00 1.60 6.060 57.00 1.40 6.322 59.00 1.60 7.480 89.00 1.30 7.650 85.00 1.30 5.345 50.00 2.40 6.883 76.00 1.80 7.082 73.00 2.10