Random samples of size
Random samples of size 100 are taken from infinite pouplation in which 20% of the items have a specific characteristic. What is that probability that the sample proportion observed in any random sample of 100 will be betwen 0.1216 and 0.2784?
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Determine the conditional probability that someone has the disease, given a positive test result? Hint: you need to be familiar with the Bayes rule and the total probability rule.
A sample of 400 observations will be taken from the infinite population. If the population proportion is 0.80, what is the probability that p-hat will be greater than 0.83?
Random samples of size 225 are taken from an infinite pouplation in which 90% of the items have a particular characteristic. What are the mean & standard deviation of the sampling distribution for p-hat?
For each given p, let Z have the binomial distribution with parameters p and N. Assume that N has binomial distribution with parameters q and M. Formulate Z as a random sum and show that Z has binomial distribution with parameters pq and M
A population consisting of 500 items has the mean of 150 and standard deviation of 25. If random samples of size 100 are taken, determine the value of the standard deviation of the sample average?
An unbiased estimator will have a value, on average, that is equal to the value of the population parameter it estimates, regardless of sample size. True or False?
A 95% confidence interval for mean, µ, of a population computed from a random sample is found to be 9 ± 3. Based on this, which of the following statements is true?
If we had 6 red balls and 6 green balls(all enumerated), and if we were randomly picking the pair of those balls, the probability of having 3 pairs of red balls only would be computed by the following formulae: (6!/((2!)^3 3!)^2 / (12!/((2!)^6 6!)
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