The following data are assessments of tuna quality. We compare the Hunter L measure of lightness (x) to the averages of consumer panel scores (y) (recoded as integer values from 1 to 6 and averaged over 80 such values) in 9 lots of canned tuna. (Hollander & Wolfe (1973), p. 187f.) Build a confidence interval for the slope parameter and use this interval to test the claim that the population slope is greater than zero at 5% significance.
X: 44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1
Y: 2.6, 3.1, 2.5, 5.0, 3.6, 4.0, 5.2, 2.8, 3.8