please answer all parts 5. The Washington Department of Transportation reported

Question

please answer all parts

5. The Washington Department of Transportation reported the following data on driving Speed (miles per hour, mph) and fuel efficiency or Mileage (miles per gallon, mpg), for ten mid-size automobiles: 1 2 3 4 5 6 7 8 9 10 Automobile Speed (mph) 30 50 40 55 30 25 60 25 50 55 Mileage (mpg) 28 25 25 23 30 32 21 35 26 25 a. Compute the sample bivariate correlation coefficient. b. Interpret the strength (magnitude) and sign (direction) of the sample bivariate correlation coefficient Test whether the population bivariate correlation coefficient differs significantly from zero at o*0.01 c. State the null and alternative hypotheses associated with the test. d. What is the calculated value of the associated test statistic? e. What is the critical value of the associated test statistic? f. State your decision regarding the null hypothesis g. State your conclusion (meaning, describe what the decision means in this problem)

Explanation / Answer

(a) r = -0.91

(b) The correlation is strong and negative. An increase in x results in a decrease in y.

(c) Ho: = 0 versus Ha: 0

(d) t = -6.223

(e) Critical t (Df = 8) is -3.3554

(f) Since -6.223 < -3.3554, reject Ho

(g) The correlation is significantly different from 0.

Regression Analysis r² 0.829 n   10 r   -0.910 k   1 Std. Error   1.874 Dep. Var. y ANOVA table Source SS   df   MS F p-value Regression 135.9187 1   135.9187 38.72 .0003 Residual 28.0813 8   3.5102 Total 164.0000 9   Regression output confidence interval variables coefficients std. error    t (df=8) p-value 95% lower 95% upper std. coeff. Intercept 39.0181 0.000 x -0.2861 0.0460 -6.223 .0003 -0.3922 -0.1801 -0.910

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