In: Statistics and Probability
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 0.01 level of significance.
number of times checked out | number of pages |
---|---|
17 | 279 |
15 | 246 |
7 | 399 |
28 | 231 |
36 | 313 |
5 | 390 |
12 | 281 |
8 | 336 |
41 | 407 |
22 | 371 |
23 | 371 |
10 | 257 |
18 | 327 |
40 | 440 |
25 | 357 |
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 0.01 the critical value is -3.012 and 3.012
The test value is: (round to 3 decimal places)
The p-value is: (round to 3 decimal places)
The decision is to
Thus the final conclusion sentence is