Question

A student wants to see if the weight of a paperback book and the number of pages in the book are related. She guesses that the weight of the book 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.

weight in ounces	number of pages
39	101
31	126
13	86
15	97
44	134
49	105
26	82
22	74
28	125
36	72
12	72
1	92
26	85
50	84
47	77

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

• 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

Y 101 126 134 105 X .Y 3939 3906 1118 1455 5896 5145 2132 1628 3500 2592 X .X 1521 961 169 225 1936 2401 676 484 784 1296 144 82 Y .Y 10201 15876 7396 9409 17956 11025 6724 5476 15625 5184 5184 8464 7225 7056 5929 74 125 864 92 1 2210 4200 3619 676 2500 2209

from given data LT=439; Ly-1412 ; [xy : 42296; Er? 15983 y 138730 correlation coefficient (7) Y- n Ery - Eusy 15 X 42296- 439 x 1412 Jon Ea? (Ly*J[ny? (ZvP] [5*45953- 4399] [15 x 138120 – 141] - 17:0.2281 (b) The equation ý = a + bxt where . Ey {X?- Ex {xy - 15 x 15983 - 439 x 42 296 D [r(Ex)2 15 x 15983 - 4392 La = 85.064 b . n Lxy - Ex Ey - 15 X 42296 - 439 x 1412 DE x2 - (Ex)2 is X15983 - 4392 T6 = 0.310) y = 85.064 + 0.310 x co) we want to test Houp=0 vs H P to 2 Jest statistic, t rt V1-72 t= 0.228 15-2 1-0.2282 t = 0.844

p-value: p (Itn-2 >0.844) - plitig! 30.844) = 0.4138 fta & - Q.414 since p-value >0.01, do not reject Ho, There is not enough evidence to reject the claim that there is a linear relationship