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Let X1,..., Xn be a random sample from a normal population. A particular realization resulted in a sample mean of 20 with the sample standard deviation 4. Construct a 95% con?dence interval for μ when:
(a) n = 5, (b) n = 10, and (c) n = 25.
What happens to the length of the con?dence interval as n changes?
Suppose X is a random variable with mean u and variance sigma2, Calculate the mean vector and variance matrix of the random vector Y = (X,2+3X)?
The company can alter the standard deviation. Use a sketch to decide how the company can proceed if they want to reduce this proportion by changing the standard deviation.
suppose that 84 of hypertensives and 23 of normotensives are classified as hypertensive by an automated blood-pressure
an educational psychologist is interested in determining whether attitudes toward school change with age. she randomly
Let f(x) be the uniform density on [0,1] and let g(x) be the density on [0,1] given by g(x)=ce^x, where c is the normalizing constant. Let F, and G be the corresponding CDFs. Find the density function corresponding to the new CDF H(x) = F(x)G(x).
For a sample with n=36, the mean duration of a geyser is 3.55 minutes and the standard deviation is 0.63 mintues. Using chebychev's theory, determine at how many of the eruptions lasted between 2.29 and 4.81 mintues.
Consider the following estimated regression equation, based on 10 observations.
Describe how to draw the sample as a cluster random sample, using flights as the cluster. Describe how to draw the sample as a systematic sample from these flights.
Determine the test sequence that minimizes the total expected cost of testing an item. Prove that your proposed sequence is optimal in minimizing the total expected cost of testing an item.
About 10% of all adults deliberately do a one-time fling and feel no guilt about it. In a group of 7 adult friends, what is the probability that: No one has done a one-time fling.
the population in millions and the violent crime rate per 1000 were recorded for 10 metropolitan areas. the data are
What percentage of normal and healthly adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 F is approproate?
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