The weights (in pounds) of 6 vehicles and the variability of their braking dista

Question

The weights (in pounds) of 6 vehicles and the variability of their braking distances (in feet) when shipping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in breaking distance on a dry surface? Use alpha = 0.01 A. The critical values are B. The critical value is Calculate the test statistic. t = (Round to three decimal places as needed.) What is your conclusion? There enough evidence at the 1% level of significance to concludes that there a significant linear correlation between vehicle weight and variability in braking distance on a dry surface.

Explanation / Answer

Solution:

We are given a following data:

X

Y

5960

1.71

5340

1.95

6500

1.95

5100

1.56

5880

1.64

4800

1.5

For the above data, we have

Correlation coefficient = r = 0.621733

Sample size = n = 6

We have to test for population correlation coefficient.

H0: = 0 versus Ha: 0

Degrees of freedom = n – 1 = 6 – 1 = 5

Level of significance = alpha = 1% = 0.01

Critical value = t = 4.6041 and -4.6041

Test statistic formula is given as below:

Test statistic = t = r*sqrt[(n – 2)/(1 – r^2)]

Test statistic = t = 0.621733*sqrt[(6 – 2)/(1 - 0.621733^2)]

Test statistic = t = 1.58761433

P-value = 0.1876

Alpha value = 0.01

P-value > Alpha value

So, we do not reject the null hypothesis that the given correlation coefficient is not statistically significant.

There is not enough evidence at the 1% level of significance to conclude that there is a significant linear correlation between vehicle weight and braking distance.

X

Y

5960

1.71

5340

1.95

6500

1.95

5100

1.56

5880

1.64

4800

1.5

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