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Question: Means, Medians, Logs, Ratios. Consider the following tuitions and their natural logs for five colleges:
(a) Find the average In-State tuition. Find the average log(In-State). Confirm that the log of the average is not the same as the average of the logs.
(b) Find the median In-State tuition and the median of the logs of In-State tuitions. Verify that the log of the median is the same as the median of the logs.
(c) Compute the median of the ratios. Compute the differences of logged tuitions-log(Outof-State) minus log(In-State) and compute the median of these differences. Verify that the median of the differences (of log tuitions) is equal to the natural log of the median of ratios (aside from some minor rounding error).
Discuss a scenario where two-sample hypothesis testing might be useful for you. Explain what a type 1 error would mean for this scenario. Explain what a type 2 error would mean.
Fitness of cardiac patients. The physical fitness of a patient is often measured by the patient's maximum oxygen uptake.
Problem: The random variable T denotes the time in second for which a firework burns before exploding. The probability density function of T is given by
You are the manager of a factory that produces Mini-Oats Cereal. The factory has an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces.
Suppose that the probability of a long-distance carrier's customer leaving for another carrier from one month to the next is 0.15. What distribution models the retention of an individual customer? What is the expected value and standard deviation?
A population of 1000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.
Assuming that the self-service times tend to be exponentially distributed, what is the probability that a customer will require more than 10 minutes to complete the job?
What should the rate of premium payment be on each policy, in order that there is a 95% chance that total premiums on all 100 policies will cover the total benefits on all policies? Use a normal approximation.
One of the products produced by Branco Food Company is Total-Bran Cereal, which competes with three other brands of similar total-bran cereals.
Is there a difference in the mean allowances nationally and the mean allowances in northwestern Ohio for nine-year-olds?
When water is poured on the top of a pile of rocks, it always trickles down to the rocks on the bottom. Similarly, when rich people make lots of money.
Given that the landowner pays for the soundings test and the test indicates that gas is present, what is the landowner's revised estimate of the probability of finding gas in this site?
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