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 13 books from the library, test her claim at a 0.10 level of significance.

number of times checked out	number of pages
6	377
18	309
44	428
39	339
28	248
14	369
10	358
25	265
36	290
43	251
12	398
33	394
50	360

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 -1.796 and 1.796

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

Test statistic is :

P-value is :

The decision is to do not reject Ho

Thus the final conclusion sentence is :

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