Question Help The weights (n pounds) of 6 vehicles and the variability of their

ID: 3218588 • Letter: Q

Question

Question Help The weights (n pounds) of 6 vehicles and the variability of their braking distances (in feet) stopping dry surface are en on a shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry Use eight, x 5960 5360 6500 5100 58 0 4800 istance, in braking 1.94 16 1.67 1.50 y Click here to view a table of critical values for Student's t-distribution. Setup the hypothesis for the test. Ho: p 0 Ha p Identify the critical value(s) select the correct choice below and fill in any answer boxes within your choice (Round to three decimal places as needed.) Click to select your answer(s)

Explanation / Answer

5960

1.77

5360

1.95

6500

1.94

5100

1.63

5870

1.67

4800

1.50

Setup the hypothesis:

H0: r = 0

Ha: r ¹ 0

The critical values are:

From t-table for4 degrees of freedom at 5% level of significance we get the critical value:

-to = -2.776 and +to = 2.776

Now we can go to excel and we go to Data. There we find Data Analysis. We select Regression and then y and x values. We get the output as below:

Regression Statistics

Multiple R

0.6590

R Square

0.4343

Adjusted R Square

0.2929

Standard Error

0.1502

Observations

ANOVA

Significance F

Regression

0.0693

3.0714

0.1546

Residual

0.0902

0.0226

Total

0.1595

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

0.6907

0.6037

1.1441

0.3164

-0.9855

2.3670

0.0002

0.0001

1.753

0.1546

-0.0001

0.0005

The test statistics:

t = 1.753

test statistics falls in the interval of -2.776 and + 2.776; we fail to reject the null hypothesis.

Conclusion:

There is not enough evidence at the 5% level of significance to conclude that there is a significant correlation between vehicle weight and variability in banking distance on a day surface.