21 A student wants to see if the number of times a book has been checked out of the library in the past yearand the number of pages in the book are related. She guesses that the number of times a book has beenchecked out of the library in the past year will be a predictor of the number of pages it has. She randomlysampled 13 books from the library, test her claim at a 0.10 level of significance.number of times checked outnumber of pages434081138214356464323036520226364343442013802730040361403169.238The correlation coefficient:r=(round to 3 decimal places)The equation y=a+bx is: (round to 3 decimal places)y=+XThe hypotheses are:Ho:p = 0 (no linear relationship)HA:P + 0 (linear relationship) (claim)Since a is 0.10 the critical value is -1.796 and 1.796The test value is:(round to 3 decimal places)The p-value is:(round to 3 decimal places)The decision is toO reject Hodo not reject HọThus the final conclusion sentence isThere 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.

Name: 21 A student wants to see if the number of times a book has been check
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 21 A student wants to see if the number of times a book has been checked out of the library in the past yearand the number of pages in the book are related. She guesses that the number of times a book has beenchecked out of the library in the past ye

As per our guidelines, we are allowed to answer three sub-parts only (1) Let X represents the Number of pages checked out Y represents the No. of Pages The correlation Coefficient : No. of Pages checked out (X) No. of Pages (Y) 43 408 11 382 14 356 46 432 30 365 20 226 36 434 34 420 1 380 27 300 40 361 40 316 9 238 KeyX: X ValuesY: Y ValuesMx: Mean of X ValuesMy: Mean of Y ValuesX - Mx & Y - My: Deviation scores(X - Mx)2 & (Y - My)2: Deviation Squared(X - Mx)(Y - My): Product of Deviation Scores Result Details & CalculationX Values∑ = 351Mean = 27∑(X - Mx)2 = SSx = 2568Y Values∑ = 4618Mean = 355.231∑(Y - My)2 = SSy = 55570.308X and Y CombinedN = 13∑(X - Mx)(Y - My) = 4992R Calculationr = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))r = 4992 / √((2568)(55570.308)) = 0.4179 The value of R is 0.4179.(2) Equation: Sum of X = 351Sum of Y = 4618Mean X = 27Mean Y = 355.2308Sum of squares (SSX) = 2568Sum of products (SP) = 4992Regression Equation = ŷ = bX + ab = SP/SSX = 4992/2568 = 1.94393a = MY - bMX = 355.23 - (1.94*27) = 302.74479ŷ = 1.94393X + 302.74479Test Static (T) = r×n-21-r2 = 0.4179×13-21-0.41792 = 1.525, where r = correlation coefficient Degrees of Freedom= 11 The test value is 1.525 The P-vale at 0.10 α is The P-Value is 0.155328. As P-value is greater than level of significance, There is no enough evidence to reject the Null Hypothesis