A student wants to investigate whether the number of times a book has been checked out from the library in the past year is related to the number of pages it has. She hypothesizes that the frequency of checkouts can predict the number of pages. The student randomly sampled 14 books from the library to test her hypothesis at a 0.05 level of significance.**Data Sample:**| number of times checked out | number of pages ||-----------------------------|-----------------|| 27 | 371 || 12 | 348 || 28 | 375 || 9 | 390 || 13 | 277 || 1 | 321 || 27 | 342 || 30 | 299 || 33 | 272 || 32 | 401 || 33 | 295 || 32 | 417 || 27 | 400 || 41 | 402 |**Statistical Analysis:**1. **Correlation Coefficient (r):** Enter the calculated value, rounded to three decimal places.2. **Equation of the Line (y = a + bx):** Find and round the values of 'a' and 'b' to three decimal places.3. **Hypotheses:** - Null Hypothesis \( H_0 \): \(\rho = 0\) (no linear relationship) - Alternative Hypothesis \( H_A \): \(\rho \neq 0\) (there is a linear relationship)4. **Critical Values:** With \(\alpha = 0.05\), the critical values are -2.179 and 2.179.5. **Test Value:** Compute and round to three decimal places.6. **P-value:** Round the calculated p-value to three decimal places.**Decision Making:**- Decide whether to reject or not reject \( H_0 \) based on the test results.**Conclusion Options:**- 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.This analysis

As given, the" number of times checked out " will be a predictor of the " number of pages ". Therefore, x = independent variable = number of times checked out y = dependent variable = number of pages. The correlation coefficient can be found using Ms-Excel. Correlation coefficient = 0.203 [ using the Excel function CORREL(range of y ,range of x) ]Step-by-step procedure to obtain the multiple linear regression equation using EXCEL is defined as follows: In Excel sheet, enter y, x in columns A, B respectively. In Data, select Data Analysis and choose Regression. Select X range and Y range. Select Labels. Click OK. Output obtained using Excel is given below: Regression equation: Y=8.637+0.046x Given, H0:ρ=0 H1:ρ≠0. Critical value is ±2.179. Test statistic: t=rn-21-r2=0.20314-21-0.2032=0.718 test statistic value is 0.718. p-value: Computation of P-value: The two tailed P-value for the t-test at 13 degrees of freedom is approximately 0.487 which can be obtained using the excel formula, “=T.DIST.2T(0.718,12)”. p-value is 0.487. Decision rule: If p-value ≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: Here, p-value (0.487) is greater than the level of significance (0.05). Therefore, fail to reject the null hypothesis. Do not reject H0. There is not enough evidence to support the claim that there is a linear relationship.