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(i) Establish that E(X) for the geometric random variable is 1/p and that V ar(X) = q/p2, where q = 1 - p.
(ii) Given that for a certain geometric random variable, P (X = 2) = 0.0475 and P (X = 10) = 0.0315, determine P (2 ≤ X ≤ 10).
(iii) The average chain length of a polymer produced in a batch reactor is given as 200 units, where chain length itself is known to be a geometric random variable. What fraction of the polymer product is expected to have chains longer than 200 units?
The new study is going to use the confidence level of 90%. The estimator or appreciative must be in 1% of the population proportion. Which is the necessary size of the sample?
consider a company that selects employees for random drug tests. the company uses a computer to randomly select
the poll claims that 70 of the population is for a new amendment. a random sample of 49 people showed that 27 voted in
in a standard normal distribution what must z be such that p-zlt z lt z
Sub-dividing Numerical Values
Find the probability of type I error if exactly 60% of the voters favor the use of these fuels. What is the type II error probability if 75% of the voters favor this action?
In a large clinical trial of 500 patients treated with a new drug, 40 reported sideeffects how many patients would need to be sampled to estimate the desired proportion to within a margin of error of 1%, using 98% confidence?
How are independent samples t-tests and One-way ANOVAs similar? How do the two tests differ and what is the F-ratio? That is, what makes up the top and bottom portions of the F-ratio?
At the .05 significance level, is the number of units produced on the afternoon shift larger?
An experimental study is designed to test the potency of a drug on 16 calves. Previous studies have shown that a 10-mg dose of the drug is lethal 7% of the time within the first 7 hours.
(i) Formulate the null and alternative hypothesis to Fruitco's management question. (ii) Conduct a hypothesis test for a single proportion at the 1% level of significance. (iii) What recommendation would you make to the Fruitco management? Justify.
In each of the following cases, decide whether or not a binomial distribution is an appropriate model, and give your reasons.
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