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It is well-known that the traditional t procedure for estimating a single mean can have poor performance in the presence of outliers. Suppose you propose a new procedure called "trim-4" where one first trims the two smallest and two largest observations from the data, and then construct the usual t interval based on the remaining n-4 observations. You are interested in exploring properties of this new method of estimating a population mean.
(a) Explicitly define your new confidence procedure including the choice of critical values.
(b) Suppose one samples from a normal distribution with mean and standard deviation a. Describe how you would use a Monte Carlo procedure to find the probability of coverage of your new confidence procedure.
(c) Using some type of variance reduction, describe an improved Monte Carlo experiment to estimate the probability of coverage.
Give as many details of the experiment us possible, and explain how you would measure the size of the variance reduction.
Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x. Make continuity corrections for each of the following, and then use the normal approximation to the binomial to find each probabili..
Explain each sampling technique discussed in the "Visual Learner: Statistics" in your own words, and give examples of when each technique would be appropriate.
What is the conditional probability that a student likes gospel music if we know that he or she likes country music?
In a 2^6 factorial form a 4 blocks with eight treatment combination. Confirm higher order interaction and any other two in such a way that generalized interaction is not violated and also 2 factor interaction and main treatment is not confounded.
A student scored 76 on a general science test where the mean and standard deviation were 82 and 8, respectively he also scored 53 on a psychology test where the class mean and standard deviation were 58 and 3, respectively. In which class was his rel..
The ratio of the two population variances.
2. The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. A random sample of 60 people used the new toothpaste for 6 months. The mean number of cavities at their next checkup is 1.5. In the ge..
Most of us love Luzon mangoes, but hate buying those that are picked too?early. Unfortunately, by waiting until the mangos are almost ripe to pick carries a risk of having 15% of the picked rot upon arrival at the packing facility.
The company must also purchase connectors from two other suppliers, 20% from B and the rest from C. The rates of defective connectors from B and C are 2% and 4% respectively. You buy one and find that it is defective. What is the probability that it ..
A child psychologist was interested in the difference in age (in years) between a boy and a girl when they first learn to ride a two-wheeled bicycle. The psychologist calculated a 99% confidence interval for the difference in age to be (-0.58, 0.71)...
The distribution of resistance for certain types of resistors (measured in ohms) is normallydistributed with mean μ and standard deviation σ. What should the value of σ be if we want tomake sure than 90% of the resistors have resistances that are wit..
Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they ..
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