Question

Annual high temperatures in a certain location have been tracked for a sample of 13 years. Let X represent the year and Y the high temperature (in C∘).

Years	Temperature in C∘C∘
2	9.5
3	9.35
4	11.2
5	11.35
6	10.6
7	12.95
8	13.7
9	13.45
10	12.2
11	12.65
12	15.9
13	15.55
14	14.3

1) Calculate the correlation coefficient. (Round to three decimal places.)
r=

Let's test the significance of the correlation coefficient at α=0.05 significance level.

H0: There is not a significant relationship between the year and high temperature, i.e., ρ=0.

Ha: There is a significant relationship between the year and high temperature, i.e., ρ≠0

1. Calculate the test statistic. Round to three decimal places.
   t=
   
2. Calculate the pp-value. Round to four decimal places.
   p-value =

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	2	9.5	4	90.25	19
	3	9.35	9	87.4225	28.05
	4	11.2	16	125.44	44.8
	5	11.35	25	128.8225	56.75
	6	10.6	36	112.36	63.6
	7	12.95	49	167.7025	90.65
	8	13.7	64	187.69	109.6
	9	13.45	81	180.9025	121.05
	10	12.2	100	148.84	122
	11	12.65	121	160.0225	139.15
	12	15.9	144	252.81	190.8
	13	15.55	169	241.8025	202.15
	14	14.3	196	204.49	200.2
Total	104	162.7	1014	2088.555	1387.8

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Conclusion: There is a significant relationship between the year and high temperature, i.e., ρ≠0