Answered: College Students' Part-Time Weekly…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

College Students' Part-Time Weekly Earnings (n = 5)

Hours Worked (X)	Weekly Pay (Y)
9	103
15	174
19	209
16	152
35	277

a) Calculate SS_xx, SS_yy, and SS_xy. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)

(b) Calculate the sample correlation coefficient. Check your work by using Excel's function =CORREL(array1, array2). (Round your answer to 4 decimal places.)

(c) Find t_.₀₂₅ for a two-tailed test for zero correlation at α=0.05α=0.05 . (Round your answer to 3 decimal places.)

(d-1) Calculate the t test statistic. (Round your answer to 3 decimal places.)

(d-2) Should we reject the null hypothesis of zero correlation?

(e) Use Excel's function =T.DIST.2T(t,deg_freedom) to calculate the two-tail p-value. (Round your answer to 4 decimal places.)

Expert Solution

Step 1

“Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get the remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”

Given:

n = 5

Formula Used:

${SS}_{xx} = \sum_{}^{} X^{2} - \frac{{(\sum_{}^{} X)}^{2}}{n}$

${SS}_{yy} = \sum_{}^{} Y^{2} - \frac{{(\sum_{}^{} Y)}^{2}}{n}$

${SS}_{xy} = \sum_{}^{} XY - \frac{\sum_{}^{} X \sum_{}^{} Y}{n}$

$Correlation coefficient r = \frac{n \sum_{}^{} XY - \sum_{}^{} X \sum_{}^{} Y}{\sqrt{[n \sum_{}^{} X^{2} - {(\sum_{}^{} X)}^{2}] [n \sum_{}^{} Y^{2} - {(\sum_{}^{} Y)}^{2}]}}$