Inference for Means Names:
Math 256
Answer the following questions. The data can be found in the Excel document
in the Math 256 folder at http://www.instruction.greenriver.edu/dnelson.
1. We have two methods for estimating the life of a tire. One method is based
on the change in weight of the tire; the other is based on the change in depth
of a grove between treads. A random sample of sixteen tires were examined and
their estimated life-span (in thousands of miles) using each method is given in
columns labeled WGT and GRO, respectively. (R. D. Stichler, G. G. Richey, and J.
Mandel, "Measurement of Treadware of Commercial Tires," Rubber Age,
73:2 (May 1953))
a) Is this a matched-pairs design, or is it a two-sample t-test?
b) How strong is the evidence supporting the claim that the grove method
predicts a shorter life span than the weight method? Give a P-value and state
whether the P-value supports the claim or supports the null hypothesis.
2. We want to know if kiln dried corn seed produces larger yields than
regular corn seed. Each type of seed was planted in 11 adjacent plots, with
alternating rows of seeds. The column labeled REG represents the yield (in
pounds per acre) of regular seed. The column labeled KILN gives the corn yield
for the kiln-dried seed. (W. S. Gosset, "The Probable Error of a
Mean," Biometrika, 6 (1908), pp 1-25.)
a) Is this a matched-pairs design, or is it a two-sample t-test?
b) How strong is the evidence supporting the claim that the kiln-dried seeds
produce a larger yield? Give a P-value and state whether the P-value supports
the claim or supports the null hypothesis.
3. The length of time between eruptions of Old Faithful Geyser appears to be
increasing. The data in WT1 is the length of time between eruptions (in minutes)
recorded between 8/1/75 and 8/10/75. The data is WT2 is the length of time
between eruptions recorded between 8/6/85 and 8/10/85. (A. Azzalini and A. W.
Bowman, "A look at Some Data on the Old Faithful Geyser," Applied
Statistics, 1990, pp 57-365.)
a) Is this a matched-pairs design, or is it a two-sample t-test?
b) How strong is the evidence supporting the claim that the eruptions are
becoming farther apart? Give a P-value and state whether the P-value supports
the claim or supports the null hypothesis.
4. In 1879, Michelson attempted to determine the speed of light. He repeated
the experiment again in 1882. Column VEL1 reports the values for the first
experiment and Column VEL2 is the measurements from the 1882 experiment. Note
that 299,000 kilometers per second has been subtracted from each measurement to
make the numbers easier to process. (S. M. Stigler, "Do Robust Estimators
Work with Real Data?" The Annals of Statistics, 1977, pp 1055-1098.)
a) Is this a matched-pairs design, or is it a two-sample t-test?
b) How strong is the evidence supporting the claim that the speed of light is
not the same in both years? Give a P-value and state whether the P-value
supports the claim or supports the null hypothesis.