Question

Assume you have noted the following prices for books and the number of pages that each book contains. Book Pages (x) Price (y) A 500 $7.00 B 700 7.50 C 750 9.00 D 590 6.50 E 540 7.50 F 650 7.00 G 480 4.50 a. Perform an F test and determine if the price and the number of pages of the books are related. Let ? = 0.01. b. Perform a t test and determine if the price and the number of pages of the books are related. Let ? = 0.01. c. Develop a 90% confidence interval for estimating the average price of books that contain 800 pages. d. Develop a 90% confidence interval to estimate the price of a specific book that has 800 pages.

Answer 1

Solution:

Using excel, we get the following output.

Regression Analysis
	r²	0.563	n	7
	r	0.750	k	1
	Std. Error	0.981	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	6.1920	1	6.1920	6.44	.0520
Residual	4.8080	5	0.9616
Total	11.0000	6
Regression output					confidence interval
variables	coefficients	std. error	t (df=5)	p-value	90% lower	90% upper
Intercept	1.0416	2.3772	0.438	.6796	-3.7486	5.8317
x	0.0099	0.0039	2.538	.0520	0.0020	0.0178

a. Null hypothesis (Ho): The price and number of pages of the books are not related.

Alternative Hypothesis (Ha): The price and number of pages of the books are related.

Test Statistics

F = 6.44

P-value = 0.052

Since p-value is greater than 0.01 level of significance, we fail to reject Ho.

Hence, we cannot conclude that the price and number of pages of the books are related.

b. Null Hypothesis (Ho): The price and number of pages of the books are not related.

Alternative Hypothesis (Ha): The price and number of pages of the books are related.

Test Statistics

t = 2.538

P-value = 0.0520

Since p-value is greater than 0.01 level of significance, we fail to reject Ho.

Hence, we cannot conclude that the price and number of pages of the books are related.

c. The regression equation is Y = 1.0416 + 0.0099X

When X = 800, the price of books would be

Y = 1.0416 + 0.0099 (800) = 8.967

90% confidence interval for for estimating the average price of books that contain 800 pages is given by:-

8.967 t (0.10, 7 - 2)*0.981*1/7 + (800 - 601.43)^2/(7 - 1) (102.5392)

8.967 2.015*0.981*0.8763

8.967 1.732

7.235, 10.699

90% confidence interval for estimating the average price of books that contain 800 pages is 7.235, 10.699

d. 90% confidence interval for for estimating the average price of books that contain 800 pages is given by:-

8.967 t (0.10, 7 - 2)*0.981*1 + 1/7 + (800 - 601.43)^2/(7 - 1) (102.5392)

8.967 2.015*0.981*1.693

8.967 3.347

5.62, 12.31

90% confidence interval to estimate the price of a specific book that has 800 pages is 5.62 to 12.31.