The table below shows the velocity y, in miles per minute, of a toy car at different times x, in minutes: Time (x) (minutes) 10
20 30 40 Velocity (y) (miles) 0.2 0.8 0.1 0.4 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and velocity of the toy car. (4 points) [Choose the value of correlation coefficient from −1, 1, −0.04, 0.99] Part B: What is the value of the slope of the graph of velocity versus time between 10 minutes and 20 minutes, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation?
1 answer:
A. If you plot the points in a graph, it would look like that shown in the picture attached. If we use linear regression, the correlation is very poor. The coefficient of correlation (r2) is only 0.0017. There is no linear relationship between time and velocity.
B. The slope of the graph is equal to y2-y1/x2-x1, In this case, it would specifically be v2-v1/t2-t1
Slope = 0.8-0.2/20-10 = 0.06 miles/s^2
The slope represents the acceleration at time 10 to 20 minutes.
C. The table in the graph shows causation rather than correlation. The points in the data occur in a sequential manner.
B. The slope of the graph is equal to y2-y1/x2-x1, In this case, it would specifically be v2-v1/t2-t1
Slope = 0.8-0.2/20-10 = 0.06 miles/s^2
The slope represents the acceleration at time 10 to 20 minutes.
C. The table in the graph shows causation rather than correlation. The points in the data occur in a sequential manner.
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Answer:
a)0.6192
b)0.7422
c)0.8904
d)at least 151 sample is needed for 95% probability that sample mean falls within 8$ of the population mean.
Step-by-step explanation:
Let z(p) be the z-statistic of the probability that the mean price for a sample is within the margin of error. Then
z(p)= where
- Me is the margin of error from the mean
- s is the standard deviation of the population
- N is the sample size
a.
z(p)= ≈ 0.8764
by looking z-table corresponding p value is 1-0.3808=0.6192
b.
z(p)= ≈ 1.1314
by looking z-table corresponding p value is 1-0.2578=0.7422
c.
z(p)= ≈ 1.6
by looking z-table corresponding p value is 1-0.1096=0.8904
d.
Minimum required sample size for 0.95 probability is
N≥ where
- N is the sample size
- z is the corresponding z-score in 95% probability (1.96)
- s is the standard deviation (50)
- ME is the margin of error (8)
then N≥ ≈150.6
Thus at least 151 sample is needed for 95% probability that sample mean falls within 8$ of the population mean.