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1.Suppose we have a random sample X1, . . . , X6 from a uniform(4,θ) distribution with pdf f(x) = 1/(θ - 4) for 4 < x < θ so that E(X) = (4 + θ)/2. (a) What is the method of moments estimator of θ? (b) Is your estimator in part (a) unbiased for θ? Justify your answer. (c) If the observed data values are 4.3 4.4 4.8 5.2 5.5 6.5 what is your estimate of θ? 2.A statistician has a data set containing n1 = 7 values of a random variable X and n2 = 6values of a random variable Y . She is interested in using the run test to test the equality ofthe distribution functions. That is, she's interested in testing: H0 : F(z) = G(z) where F(z) and G(z) are the cdfs for X and Y , respectively. (a) She decides to reject H0 if the number of runs R ≤ 3. What is the significance level ofher test? In other words, what is the probability of rejecting H0 if it's true? (b) If the observed samples for X and Y are as follows, what is the statistician's conclusion? ordered x sample: 3.5 4.3 4.7 5.3 5.4 5.5 6.0 ordered y sample: 4.8 5.1 6.1 6.2 6.5 6.7
The cost accountant for Blue Pharmaceuticals has informed you that the company's materials quantity variance for the drug Allegro was exactly equal to its materials price variance for the year.
If you had only one minute to estimate the standard deviation of a frequency distribution using only the information that can be obtained from a stem and leaf display, how would you do it and why?
State your hypothesis, draw your curves, label your critical values and your test statistic, state your decision to accept or reject and write your conclusion in the language of the problem. Use a=0.05.
Use the population mean and standard deviation to find the z-score corresponding to 14.5%, the rate offered by the Bar Harbor Bank and Trust Company. Is this above or below the average?
The specification limits are set between 15.8 and 16.2 ounces.
Describe the methods for interpretation of categories (row or column) in CA. Can categories always be directly compared based on proximity in the perceptual map?
In the past, Judy Holmes's tire dealership sold an average of 1,000 radials each year. In the past two years, 200 and 250, respectively, were sold in fall, 350 and 300 in winter, 150 and 165 in spring, and 300 and 285 in summer.
Make a plot of the ratio of the number of boys born per year to the number of girls in the U.S. What do you see? In what year did we see the most total number of births in the U.S.?
Can the company conclude that the pill is effective at promoting weight loss? Write the hypotheses and conduct the appropriate hypothesis test.
Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100. a) What is the probability that a randomly selected applicant scores between 425 and 575?
What is the 'Equally-likely Outcomes Model of Probability?" What is the formula for this model of probability?
What is a 99% confidence interval for the true proportion of dentists in the population that would make such a recommendation?
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