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(a) Calculate SSxx, SSyy, and SSxy. (Leave no cells blank - be certain to enter

ID: 3318734 • Letter: #

Question

(a) Calculate SSxx, SSyy, and SSxy. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.) Picture Click here for the Excel Data File College Student Weekly Earnings in Dollars (n = 5) Hours Worked (X) Weekly Pay (Y) formula56.mml formula57.mml formula58.mml 9 98 81 7022.44 754.2 12 186 36 17.64 -25.2 16 203 4 449.44 -42.4 18 159 0 519.84 0 35 263 289 6593.44 1380.4 410 14602.8 2067 formula253.mml formula254.mml SSXX SSyy SSxy (b) Calculate the sample correlation coefficient. Check your work by using Excel's function =CORREL(array1,array2). (Round your answer to 4 decimal places.) r (c) Find t0.025 for a two-tailed test for zero correlation at formula40.mml. (Round your answer to 3 decimal places.) t.025 ± (d-1) Calculate the t test statistic.(Round your answer to 3 decimal places.) tcalc (d-2) Should we reject the null hypothesis of zero correlation? Yes No (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.) p-value

Explanation / Answer

Solution:

a.

SSxx = (X – X-bar)^2 = 410

SSyy = (Y – Y-bar)^2 = 14602.8

SSxy = (X – X-bar) (Y – Y-bar) = 2067

b. Sample correlationcoefficient, r = SSxy/SSxx*SSyy

r = 2067/410*14602.8

r = 0.8448

Using excel, =correl function, r = 0.8448

c. Degrees of freedom, d = n - 2 = 5 - 2 = 3

Using t-tables,

t (0.025, 3) = ±3.182

d-1. Test Statistic

t = r n - 2)/1 - r^2

t = 0.84483/1 - (0.8448)^2

t = 2.735

d-2: No, because test statistics lie within the critical values. Therefore, we fail to reject the Ho.

e. Using excel, the p-value is

=T.DIST.2T(2.735,3)

= 0.0716

X Y SSxx Ssyy Ssxy 9 98 81 7022.44 754.2 12 186 36 17.64 -25.2 16 203 4 449.44 -42.4 18 159 0 519.84 0 35 263 289 6593.44 1380.4 Total 90 909 410 14602.8 2067 Mean 18 181.8