Question

What is the p value of the hypothesis to test that the correlation is different from zero (Please enter in decimals. Values less than 0.001 should be entered as 0.)

Title	2013 Gross ($M)	2014 DVD Revenue ($M)
The Hunger Games: Catching Fire	407.140	54.925
Despicable Me 2	367.957	34.813
Frozen	296.692	185.483
Man of Steel	291.046	29.803
Gravity	255.622	24.350
Fast and Furious 6	238.680	11.446
The Hobbit: The Desolation of Smaug	229.060	34.679
Thor: The Dark World	203.449	27.323
World War Z	202.360	7.287
The Heat	159.582	6.842
The Wolverine	132.557	9.909
Cloudy with a Chance of Meatballs 2	117.614	20.962
Lee Daniels' The Butler	116.294	24.208
Captain Phillips	104.835	17.344
Jackass Presents: Bad Grandpa	101.625	12.768
Disney Planes	90.283	10.879
The Lone Ranger	89.290	9.432
American Hustle	87.923	8.628
The Best Man Holiday	70.493	14.121
Percy Jackson: Sea of Monsters	68.518	12.014
The Wolf of Wall Street	63.125	16.115
Last Vegas	63.112	8.999
Ender's Game	61.657	12.975
Saving Mr. Banks	58.958	13.939
Free Birds	54.895	13.002
RED 2	53.263	7.401
Tyler Perry's A Madea Christmas	50.227	10.425
The Secret Life of Walter Mitty	45.471	7.934
Riddick	42.025	13.241
The Hobbit: An Unexpected Journey	39.169	8.056
12 Years a Slave	38.472	15.233
Walking with Dinosaurs	31.344	7.529
Escape Plan	25.064	9.111
The Book Thief	19.092	9.133
About Time	15.324	7.281
The Wizard of Oz	5.509	5.538
Pitch Perfect	0.345	10.019
Lone Survivor	0.327	22.784

Answer 1

Ʃx =	4298.399
Ʃy =	755.931
Ʃxy =	145463.0664
Ʃx² =	888948.0983
Ʃy² =	47004.16858
Sample size, n =	38
x̅ = Ʃx/n = 4298.399/38 =	113.1157632
y̅ = Ʃy/n = 755.931/38 =	19.89292105
SSxx = Ʃx² - (Ʃx)²/n = 888948.09828 - (4298.399)²/38 =	402731.41504
SSyy = Ʃy² - (Ʃy)²/n = 47004.16858 - (755.931)²/38 =	31966.49288
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 145463.06642 - (4298.399)(755.931)/38 =	59955.35446

Null and alternative hypothesis:

Ho: ρ = 0

Ha: ρ ≠ 0

n = 38

Correlation coefficient, r = SSxy/√(SSxx*SSyy)

= 59955.35446/√(402731.41504*31966.49288) = 0.5284

Test statistic :  

t = r*√(n-2)/√(1-r²) = 0.5284 *√(38 - 2)/√(1 - 0.5284²) = 3.7344

df = n-2 = 36

p-value = T.DIST.2T(ABS(3.7344), 36) = 0.0006

Conclusion:

p-value < α Reject the null hypothesis. There is a correlation between x and y.