Leonard is studying the relationship between the fuel efficiency in miles per gallon (mpg), y, and the speed in miles per hour (
mph), x, of his car. He collected data for 8 different speeds and found a linear model that best fit his data: y = 18.46 + 0.16x. To analyze the fit, he found the residuals and created the following residual plot.
Using the residual plot, what conclusion can he make about the linear model he found?
A. There is a negative linear relationship between the speed and fuel efficiency.
B. There is a positive linear relationship between the speed and fuel efficiency.
C. There is a quadratic relationship between the speed and fuel efficiency.
D. There is a nonlinear relationship between the speed and fuel efficiency.
Using the residual plot, what conclusion can he make about the linear model he found?
A. There is a negative linear relationship between the speed and fuel efficiency.
B. There is a positive linear relationship between the speed and fuel efficiency.
C. There is a quadratic relationship between the speed and fuel efficiency.
D. There is a nonlinear relationship between the speed and fuel efficiency.
1 answer:
Answer:
D. There is a nonlinear relationship between the speed and fuel efficiency.
Step-by-step explanation:
A desirable residual plot should show a horizontal band with points randomly distributed about the horizontal axis.
Leonard's plot is definitely nonlinear.
The residuals show a good fit to a parabola.
This suggests that the relation between speed and fuel efficiency may be parabolic.
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Answer:
Probability that the sample proportion will be greater than 0.5 is 0.8133.
Step-by-step explanation:
We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.
Suppose that the polling organization takes a simple random sample of 500 voters.
<em>Let </em><em> = sample proportion</em>
The z-score probability distribution for sample proportion is given by;
Z = ~ N(0,1)
where, = sample proportion
p = population proportion = 48%
n = sample of voters = 500
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample proportion will be greater than 0.5 is given by = P( > 0.50)
P( > 0.50) = P(
<
) = P(Z < 0.89) = 0.8133
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.</em>
Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.