eedlings of understory trees in mature tropical rainforests must survive and grow using intermittent flecks of sunlight. How does the length of exposure to these flecks of sunlight (fleck duration) affect growth? Researchers experimentally irradiated seedlings of the Southeast Asian rainforest tree with flecks of light of varying duration while maintaining the same total irradiance to all the seedlings. Below is the data. Fit a linear model to the data. Tree Mean Fleck (min) Relative growth rate (mm/mm/week 1 3.4 0.013 2 3.2 0.008 3 3 0.007 4 2.7 0.005 5 2.8 0.003 6 3.2 0.003 7 2.2 0.005 8 2.2 0.003 9 2.4 0 10 4.4 0.009 11 5.1 0.01 12 6.3 0.009 13 7.3 0.009 14 6 0.016 15 5.9 0.025 16 7.1 0.021 17 8.8 0.024 18 7.4 0.019 19 7.5 0.016 20 7.5 0.014 21 7.9 0.014   a)What is the rate of change in relative growth rate per minute of fleck duration? Also, provide a standard error of your estimate.        (b) Use these data, test the hypothesis that fleck duration affects seedling growth rate.

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.8 8.2 6.8 3.5 2.8 2.8 2.3 0.5 y 13.9 10.8 10.1 7.2 6.5 6.5 6.3 4.8 x = thousands of automatic weapons y = murders per 100,000 residents This data can be modeled by the equation y = 0.81x + 4.35. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator. A) How many murders per 100,000 residents can be expected in a state with 7 thousand automatic weapons? Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 7.8 thousand automatic weapons? Answer = Answer = Round to 3 decimal places.

Below is a scatterplot of a student’s SAT score and their college GPA. Suppose we want to decide if a student’s SAT score and their GPA are linearly related.  What does this scatterplot tell us of the relationship?  Support your answer. SAT score_GPA scatterplot.pdf

Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. Predictor Coef SE Coef T P Constant -0.212 2.429 -0.09 0.929 Diameter 0.7527 0.1686 5.33 0.013 S = 4.16190 R-Sq = 81.2%         (c) The formula for the margin of error E for a c% confidence interval for the slope ? can be written as E = tc(SE Coef). The Minitab display is based on n = 12 data pairs. Find the critical value tc for a 90% confidence interval in the relevant table. Then find a 90% confidence interval for the population slope ?. (Use 3 decimal places.) tc   lower limit   upper…