Question

In: Statistics and Probability

the data on ages (in years) and prices (in hundreds of dollars) for 8 cars of...

the data on ages (in years) and prices (in hundreds of dollars) for 8 cars of a specific model are given:

Age: 8 3 6 9 2 5 6 3
price: 45 210 100 33 267 134 109 235

Fund the linear correlation coefficient r. Use appropriate test to indicate if there is a linear correlation.

Solutions

Expert Solution

(a)

From the given data,the following Table is calculated:

X Y XY X2 Y2
8 45 360 64 2025
3 210 630 9 44100
6 100 600 36 10000
9 33 297 81 1089
2 267 534 4 71289
5 134 670 25 17956
6 109 654 36 11881
3 235 705 9 55225
Total = 42 1133 4450 264 213565

Correlation Coefficient (r) is given by:

(b)

H0:Null Hypothesis: = 0

HA: Alternative Hypothesis: 0

Test statistic is given by:

Take = 0.05

ndf = n - 2 = 8 - 2 =6

From Table, critical values of t = 2.4469

Since the calculated value of t = - 14.3798 is less than critical value of t = - 2.4469, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that there is a linear correlation.


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