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

Required:

a.	Perform an F test and determine if the price and the number of pages of the books are related. Let a = 0.01.
b.	Perform a t test and determine if the price and the number of pages of the books are related. Let a = 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.

.

Please solve it without excel formula

Answer 1

## Using R software

Pages_x=c(500,700,750,590,540,650,480)
Price_y=c(7.00,7.5,9,6.5,7.5,7,4.5)
## a)
model_aov=aov(Price_y~Pages_x)
summary(model_aov)

# The calculated F test statistic is 6.439 with corresponding p-value 0.052.
# The p-value is greater than 0.01 significance level. Hence, we can conclude
# that the price and the number of pages of the books are not related.

## b)
model_lm=lm(Price_y~Pages_x)
summary(model_lm)

# The calculated F test statistic is 2.538 with corresponding p-value 0.052.
# The p-value is greater than 0.01 significance level. Hence, we can conclude
# that the price and the number of pages of the books are not related.

## c.
predict(model_lm, data.frame(Pages_x=800), level=1-0.10, interval = "confidence")

# 90% confidence interval for estimating the average price of books
# that contain 800 pages is (8.967278, 10.69882).

## d.
predict(model_lm, data.frame(Pages_x=800), level=1-0.10, interval = "prediction")

# 90% confidence interval to estimate the price of a specific book that
# has 800 pages is (8.967278, 11.59459).

# End