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A statistician wants to estimate the mean height h (in meters) of a population, based on n independent samples X1, . . . , Xn, chosen uniformly from the entire population. He uses the sample mean Mn = (X1 +···+Xn)/n as the estimate of h, and a rough guess of 1.0 meters for the standard deviation of the samples Xi.
a) How large should n be so that the standard deviation of Mn is at most 1 centimeter?
b) How large should n be so that Chebyshev's inequality guarantees that the estimate is within 5 centimeters from h, with probability at least 0.99?
A sample of ten ER patients was conducted to determine their average wait time and to compare this to the target wait time. The hospital wants to make sure that patients do not wait more than 35 minutes. Test following hypotheses using a 95% con..
Assume the reliability of a product is given by an exponential distribution with a mean of 1 year. How long would it take to achieve a 10% failure rate?
Test the hypotheses that the average household income in the township is greater than $100,000. Hint: Start by stating the null and alternative hypotheses.
Assuming the population variances from both offices are equal, is there evidence of a difference in the mean waiting time between the two offices? Use α = 0.05
The height of a tree will be measured using a clinometer. For this device, the measurement error has a normal distribution with mean meter and standard deviation . If the tree is exactly 35 meters tall, what is the probability that the clinometer ..
Iit is known that signal change in this brain area is normally distributed with mean of 35 and standard deviation of 10. By using .01 level, what must researcher conclude?
Think of a case in which regression analysis was used, but not properly. For instance, discuss situations in which regression analysis is not appropriate and does not add useful information to our understanding of a set of data.
The sample mean of the accounts is found to be y-bar = $94.22, and the sample variance is equal to $455.21. Estimate mu and place a bound on the error of estimation.
Does drug have significant effect on aggression? Use an alpha level of .05, two tails.
Richard is one of test takers. Find out the number of questions he can expect to get right on test by random guessing.
Does this sample give sufficient evidence to conclude that self-esteem scores for group-participation adolescents are significantly different from those of general population? Use two-tailed test with α = .01.
The availability of venture capital provided by big boost in funds available to companies recent years. According to Venture Economics, 2,000 venture capital disbursements were made in 1999.
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