Question

In: Statistics and Probability

A student wants to see if the number of times a book has been checked out...

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 14 books from the library, test her claim at a 0.05 level of significance.

number of times checked out number of pages
22 356
16 378
3 262
24 225
28 254
4 393
2 376
9 254
20 284
15 230
40 424
26 356
9 381
15 403


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 0.05 the critical value is -2.179 and 2.179

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.

Solutions

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