Question

3.         A particular Intersession stats prof is noted for 2 things: the number of pages of notes his students have to write down each night and the number of pieces of chalk he destroys each night. To see if there is any relationship between these, a record is kept of the number of pages of notes his students write during 6 different lectures in June and the number of pieces of chalk the prof destroys on these nights. The following data were obtained:

                        Night                           # Note Pages               # Chalks Destroyed

                        Monday                                   8                                  5

                        Tuesday                                  4                                  1

Wednesday                             12                                7

                        Monday                                   6                                  4

                        Tuesday                                  9                                  8

Wednesday                             7                                  2

a) Is there a significant positive correlation between # of note pages and # of pieces of chalk destroyed (α # .05)? [10 points]

b) How many pieces of chalk would the prof be predicted to destroy on a night that his students write down 10 pages of notes, and what are the 95% bounds to the error of this prediction? [10 points]

Answer 1

(a) The hypothesis being tested is:

H₀: ρ = 0

H_a: ρ ≠ 0

The correlation is 0.829.

The critical r-value is 0.811.

Since 0.829 > 0.811, we can reject the null hypothesis.

Therefore, we can conclude that there is a significant positive correlation between # of note pages and # of pieces of chalk destroyed.

(b) 6.438 pieces of chalk would the prof be predicted to destroy on a night that his students write down 10 pages of notes.

The 95% confidence interval is between 3.776 and 9.099.

The 95% prediction interval is between 0.984 and 11.891.

	r²	0.686
	r	0.829
	Std. Error	1.715
	n	6
	k	1
	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	25.7411	1	25.7411	8.76	.0416
Residual	11.7589	4	2.9397
Total	37.5000	5
Regression output					confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	-1.8661
x	0.8304	0.2806	2.959	.0416	0.0513	1.6095
Predicted values for: y
		95% Confidence Interval		95% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
10	6.438	3.776	9.099	0.984	11.891	0.313