1 answer

You wish to determine if there is a positive linear correlation between the two variables at...

Question:

You wish to determine if there is a positive linear correlation between the two variables at a significance level of α=0.001α=0.001. You have the following bivariate data set.

x y
79.4 93.7
54.6 26.9
42 70.2
86.2 84.2
117.9 139.4
51.9 45.4
56.3 69.3
75.7 64.7
59.7 114.5
72.4 51.6
49.9 35.8
93.9 84.4
27.1 29.1
91.9 117.6
55.6 42.8
85.5 125.1
84.4 121.4
105.1 142.3
72.6 37.7
84.5 34.5
101.2 117.9
82.1 131.1
128.4 117.9
97.8 128.6
105.9 75.9
28.7 7.6
60 98.1
90.3 89.3
78.2 96.4
72.2 60.7
65.9 33.1


What is the correlation coefficient for this data set?
r = Incorrect
To find the p-value for a correlation coefficient, you need to convert to a t-score:

t=√r2(n−2)1−r2t=r2(n-2)1-r2

This t-score is from a t-distribution with n–2 degrees of freedom.

What is the p-value for this correlation coefficient?
p-value = Incorrect

We were unable to transcribe this image
We were unable to transcribe this image

Answers

(a) The computation for the data: 6304.36 2981. 16 1764 7430.44 13900.41 2693.61 3169.69 5730.49 3564.09 5241.76 2490.01 8817.21 734.41 8445.61 3091.36 7310.25 7123 36 11046.01 5270.76 7140.25 10241.44 6740.41 16486.56 9564.84 11214.81 823.69 7439.78 1468.74 2948.4 7258.04 16435.26 2356.26 3901.59 4897.79 6835.65 3735.84 1786.42 7925.16 788.61 10807.44 2379.68 10696.05 0246,16 14955.73 2737.02 2915.25 11931.48 10763.31 15138.36 12577.08 8037.81 218.12 5886 8063.79 7538.48 4382.54 2181.29 8779.69 4928.04 7089.64 19432.36 2061.16 4802.49 4186.09 13110.25 2662.56 1281.64 7123.36 13829.76 1831.84 15650.01 14737.96 20249.29 1421.29 1190.25 13900.41 17187.21 13900.41 16537.96 5760.81 57.76 9623.61 7974.49 9292.96 3684.49 1095.61 105.9 8154.09 6115.24 5212 84 4342.81 ΣΧ,-23573 ΣΥ,-2487 2 ΣΧ-196746 Σ r-244953.8 ΣΧΧ-209233. 1 i-1l The corr elati on coefficient is given by 31 209233.1)-(2357.3) (2487.2) 31 196746)-(573(31(244953.8)-(2487.2 6099125-5556863) (7593568-6186164) 542261.8) 1407405) 6486227-5863077 623150.5 623150.5 63181712731 6231505 = 873602.7202 0.713311 0. 71 33 Therefore, the correlation coefficientisr 0.7133

(b) Step1 Thet -test for the Correlation Coeffi cient is We can use the correlation coefficient to determine whether there is a stati sti cally significant linear relati onship between X andY Step2:To do so, you hypothesize that the popul ati on correlation coefficient, pis 0 Thus, the null and alternative hypotheses are Ho p-0 (no correlation) versus H1 : #0 (correlation) Step3:The test statistic for determining the existence of a significant correlation. TESTING FOR THE EX STENCE OF CORRELATION 0.713311-0 1-(0.713311) 31-2 0.713311 1-0.508813 29 0.713311 0.491187 29 0.713311 0.016937 0.713311 0.130144 5.480931 = 5.480931 Step4:The P- value approach The P - value is 2P (t25.480931) 2(1-P(ts5.480931) 2(1-0.999996665) = 2(0.0000033) 0.0000067 P- value 0.0000067<0.001.</p><p>We reject the null hypothesis H. Step5:Conclusion Using, the 0.001 level of significance, because the test stati stic is t-5.4809 > t We reject the null hypothesis H,o Hence, we conclude that there is evidence of significant linear rel ati onship between the two quanti tative variables (x) and (y 4001,29 = 3.659405

.

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