Refer to Exercises 6 and 8.

a. Find the critical value for a 90% confidence interval for the slope of the true regression line. Then calculate the confidence interval.

b. Interpret the interval from part (a).

c. Explain the meaning of “90% confident” in this context.

Exercises 6 and 8.

Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. On each of four occasions, the researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He randomly assigned young perch to 1 of 4 pens so that one pen had 10 perch, one pen had 20 perch, one pen had 40 perch, and the final pen had 60 perch. Then he dropped the nets protecting the pens, allowing bass to swarm in, and counted the number of perch killed after two hours.4 A regression analysis was performed on the 16 data points using x = number of perch in pen and y = proportion of perch killed. Here is a residual plot and a histogram of the residuals. Check whether the conditions for performing inference about the regression model are met.

Transcribed Image Text:

0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 10 20 30 40 50 60 Number of perch 4 3. 1 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Residual Residual Frequency 2.