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What distribution would you use to model these data (e.g., is the normal distribution

appropriate, or other distributions seen in class)? Do you notice any skewness? Is it positive

or negative? Write 2-3 sentences for each variable to describe the distribution and which

distribution would be appropriate for the data.

Optional (extra credit): Test for normality using Minitab or Excel.

2. Suppose you were asked to model the hydraulic conductivity sample with a lognormal

distribution.

a. Estimate the parameters and o for the corresponding lognormal distribution

based on the mean and variance estimates from the sample.

b. Using the lognormal distribution you found above, find the probability that the

hydraulic conductivity takes a value between the first quartile and third quartile

values observed in the data set.

c. Briefly analyze this probability value. What would you have expected the

probability to be? How does this calculated value compare? Explain why this

difference occurs in your own words (1-2 sentences).

3. Briefly explain (1-2 sentences) what assumptions must be met to compute a confidence

interval?

4. Focusing on the porosity:

a. Find a 95% confidence interval for the mean porosity of the sample and then briefly

explain the meaning (interpret) of the 95% confidence interval.

b. Find a 99% confidence interval for the mean porosity of the sample and then briefly

explain the meaning (interpret) of the 99% confidence interval./nc. Compare the two confidence intervals (95% confidence and 99% confidence).

Explain the trade-off that occurs when increasing the confidence. Which confidence

interval would you prefer to use in the case of this data set? Briefly explain your

reasoning.

d. The New Mexico State DOT would like to have a 99% confidence interval where

the margin of error is the same as that of the 95% CI in your current sample.

Assuming that the budget they give you for sample collection is proportional to the

number of samples collected, what is the budget increase (in percent) that you need

to request to achieve this improved result in a future study? State any additional

assumptions you make in determining this value.

Hint: The increase in budget is equivalent to the increase in the number of samples

from the current to the future study.

e. Find the 95% prediction interval for a single measurement of porosity and then

briefly explain the meaning (interpret) of the 95% prediction interval.

Note: Do some research on this question!

Prediction intervals were not covered in class. Follow the textbook chapter 5.9.

f. Compare the 95% confidence interval (from part a) and the 95% prediction interval

(from part e). What is the difference between the two? Which interval is wider?

Briefly explain why.

5. Find a 99% confidence interval for the mean hydraulic conductivity of the sample. Explain

your process and reasoning.

6. In your research, you find that another firm has conducted a similar field sampling

campaign and collected soil embarkment data for porosity from 80 samples in Georgia.

The soil there is known to be mostly clay, and the firm reports a mean porosity of 0.55 in

their sample with standard deviation of 0.035.

a. Find the 95% confidence interval for the difference between the mean porosity in

New Mexico (your sample) and Georgia?

b. State your assumptions in the calculation above.

c. Interpret the meaning of the confidence interval you found above. Explain what

information it gives about the soil porosity in the two states.

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