An engineer wishing to determine whether there is a statistically significant difference between the average speed of passenger cars and that of large trucks on a section of highway, collected the data shown below. Determine whether the engineer can conclude that the average speed of large trucks is the same as for passenger cars.
What will be an ideal response?
To determine whether the difference in mean speeds was statistically significant, first, the pooled standard deviation must be determined, using Equation 4.7.
Then, compare the absolute value of the difference of the sample means with the product of the appropriate z-statistic and the pooled standard deviation.
Absolute difference in means = 73 – 70 = 3.
ZSd = (1.96)(0.64)
3 > 1.25
Therefore, a statistically significant difference exists between the two data sets, and it cannot be concluded that the average speed of large trucks is the same as that of passenger cars.
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