A sample of 84 cars from an online information service was examined to see how f
ID: 3291808 • Letter: A
Question
A sample of 84 cars from an online information service was examined to see how fuel efficiency (as highway mpg) relates to the cost (manufacturer's suggested retail price in dollars) of cars. Scatterplots and computer outputs are provided in the accompanying table. Complete parts a) through c) below. Click the icon to view the scatterplots and computer output a) State what a researcher would want to know, identify the variables, and give the appropriate hypotheses. What would a researcher want to know? A. O B. C. If there is a linear association between Price and Highway MPG in cars If Price causes Highway MPG to go up If Price causes Highway MPG to go down D. If Highway MPG causes Price to go up O E. If Highway MPG causes Price to go down What are the variables? Select all that apply A. Coefficient C. Price E. Intercept G. Highway Predicted B· D. t-Ratio Highway Residual P-Value F. H. Highway MPG What are the appropriate null and alternative hypotheses? b) Check the assumptions and conditions The Quantitative Data Condition is Normal Condition is | the Linearity Condition is | the Randomization Condition is | the Equal Spread Condition is | the Nearly and the Outlier Condition isExplanation / Answer
Here dependent variable is Highway MPG and independent variable is MSRP.
We have given the regression output with sample size 84.
What would a research want to know?
If there is linear association between price and highway MPG in cars.
Here we have to test the hypothesis that,
H0 : There is no relationship between price and Highway MPG in cars .
H1 : There is relationship between price and Highway MPG in cars.
Assume alpha = level of significance = 0.05
The test statistic follows t-distribution with n-2 degrees of freedoms.
The test statistic is,
t = r*sqrt(n-2) / sqrt(1-r2)
where r is sample correlation between two variables.
n is number of data pairs.
We also use test statistic,
t = b / SEb
where b is sample slope of independent variable or coefficient of independent vaariable.
SEb is standard error of that coefficient.
What are the variables? Select all that apply.
Therefore we need coefficient, t-ratio and p-value.
We see in the output that,
test statistic = -5.897
P-value = 0.0001
P-value < alpha
Reject H0 at 5% levelof significance.
Conclusion : There is sufficient evidence to say that there is relationship between price and Highway MPG in cars.
c) First option is correct.
ALso scatter plot shows that there is strong negative relationship between the two variables.