Highway engineers in Ohio are painting white stripes on a highway. The stripes are supposed to be approximately 10 feet long. However, because of the machine, the operator, and the motion of the vehicle carrying the equipment, considerable variation occurs among the stripe lengths. Engineers claim that the variance of stripes should be less than 16 inches squared. At α = .05, use the sample lengths given here from 12 measured stripes (in feet and inches) to test the variance claim. Assume stripe length is normally distributed. (in feet) (in inches) 9.85 118.2 9.7 116.4 9.9 118.8 9.5 114 9.15 109.8 10.1 121.2 10 120 9.8 117.6 9.9 118.8 10.3 123.6 10.1 121.2 10.2 122.4 The appropriate test for this question is: a Z-test for the true variance of stripe length. a t-test for the true mean of stripe length. a Chi-square test for the true mean of stripe length. a Chi-square test for the true variance of stripe length. The appropriate test to answer the question about the claim should be: a right-hand-side tailed test. a left-hand-side tailed test. a two-tailed test. Can’t decide. The p-value for this test is 0.46687. Is the claim that the variance of stripe length is less than 16 inches squared true or not, at 5% level of significance? True. Data evidence does not support the claim. Don’t know.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Highway engineers in Ohio are painting white stripes on a highway. The stripes are supposed to be approximately 10 feet long. However, because of the machine, the operator, and the motion of the vehicle carrying the equipment, considerable variation occurs among the stripe lengths. Engineers claim that the variance of stripes should be less than 16 inches squared. At α = .05, use the sample lengths given here from 12 measured stripes (in feet and inches) to test the variance claim. Assume stripe length is
|
(in feet) |
(in inches) |
|
9.85 |
118.2 |
|
9.7 |
116.4 |
|
9.9 |
118.8 |
|
9.5 |
114 |
|
9.15 |
109.8 |
|
10.1 |
121.2 |
|
10 |
120 |
|
9.8 |
117.6 |
|
9.9 |
118.8 |
|
10.3 |
123.6 |
|
10.1 |
121.2 |
|
10.2 |
122.4 |
- The appropriate test for this question is:
- a Z-test for the true variance of stripe length.
- a t-test for the true mean of stripe length.
- a Chi-square test for the true mean of stripe length.
- a Chi-square test for the true variance of stripe length.
- The appropriate test to answer the question about the claim should be:
- a right-hand-side tailed test.
- a left-hand-side tailed test.
- a two-tailed test.
- Can’t decide.
- The p-value for this test is 0.46687. Is the claim that the variance of stripe length is less than 16 inches squared true or not, at 5% level of significance?
- True.
- Data evidence does not support the claim.
- Don’t know.
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