A figure shows body mass in g on the x-axis and flipper length in cm on the y-axis for 68 Chinstrap penguins. The correlation coefficient r=0.64.

1. Test the null hypothesis that flipper length and body mass are uncorrelated. Use significance level at a = 0.05, and a non-directional (two-sided) alternative hypothesis. Calculate (or bound) the p-value, and clearly state your conclusion.

2. The solid black line in the graph given is the least squares line. The dashed blue line in the figure is parallel to the black least squares line and is 7 cm below it. Assume the conditions of the linear model are satisfied. Further assume the standard deviation of the residuals is 5.5 cm. If we add a new data point (the flipper length and body mass of an additional Chinstrap penguin not included in the original dataset) to the figure, what is the probability that this new data point will be BELOW the dashed blue line?

3. Next we decide to change the body mass units from grams to ounces (1 g = 0.035 ounces). We leave the flipper length units in cm. Calculate the correlation coefficient r after we have changed the body mass units to ounces.