Question

A student wants to see if the number of times a book has been checked out of the library in the past year and the number of pages in the book are related. She guesses that the number of times a book has been checked out of the library in the past year will be a predictor of the number of pages it has. She randomly sampled 15 books from the library, test her claim at a 0.10 level of significance.

number of times checked out	number of pages
17	302
5	395
20	289
6	272
7	219
41	433
25	252
18	239
12	265
2	204
13	344
33	398
3	386
34	373
44	301

The correlation coefficient:

r= (round to 3 decimal places)

The equation y=a+bx is: (round to 3 decimal places)

y=+ x

The hypotheses are:

H0:ρ=0H0:ρ=0 (no linear relationship)
HA:ρ≠0HA:ρ≠0 (linear relationship) (claim)

Since αα is 0.10 the critical value is -1.771 and 1.771

The test value is:  (round to 3 decimal places)

The p-value is:  (round to 3 decimal places)

The decision is to

• reject H0H0
• do not reject H0H0

Thus the final conclusion sentence is

• There is enough evidence to reject the claim that there is a linear relationship.
• There is not enough evidence to reject the claim that there is a linear relationship.
• There is enough evidence to support the claim that there is a linear relationship.
• There is not enough evidence to support the claim that there is a linear relationship.

Answer 1

The statistical software output for this problem is :

r = 0.390

y = 273.736 + 2.021 x

Test statistics = 1.525

P-value = 0.151

do not reject H0

There is not enough evidence to support the claim that there is a linear relationship