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- The molecular weight of a particular polymer should fall between 750 and 1,035. Thirty samples of this material were analyzed with the results X-bar = 902 and s = 90. Assume that molecular weight is normally distributed.Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?Records for the last 15 years have shown that the average rainfall in a certain region of the country, for the month of March, to be 1.20 inches, with s = 0.45 inches. A second region had an average rainfall of 1.35 inches, with s = 0.54. estimate the difference of the true average rainfalls in those two regions as a 95% C.I. with the assumption of normal populations and unequal variances.
- Based on a random sample of 25 units of product X, the average weight is 102 lbs., andthe sample standard deviation is 10 lbs. We would like to decide if there is enough evidenceto establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.what is the critical value to test the claim at (alpha)= ,01?The average number of pounds of sliced ham ordered per customer at the deli where Dennis used to work was 1.4, but at his new job, the average of the 32 people who have ordered ham so far is 1.5 pounds, with a standard deviation of 0.3 pounds. a) Write the null and alternative hypotheses to test if the average amount of ham bought is higher at the new store. H0:μ= H1:μ> b) For α=0.025, find the rejection region in terms of z. [Write your answer with 2 decimal places.] R:z≥ c) What test statistic corresponds to an x¯ of 1.5 pounds? [Round your answer to 2 decimal places.] z= d) Should you reject the null hypothesis?Suppose that the lifetime, X, and brightness, Y, of a light bulb are modeled as continuous random variables. Let their joint pdf be given by:f(x,y)=λ_1λ_2e^{-λ_1x-λ_2y},x,y>0 •Are lifetime and brightness independent?•Are lifetime and brightness uncorrelated?
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- Suppose that X1, . . . , Xn is a random sample from the Normal distribution N (0, σ2 ) with parameter σ > 0, Find the Maximum Likelihood Estimation of σ.If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?A researcher is testing the effect of a new cold and flu medication on reaction time. A sample of n = 16 students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student's reaction time is measured. The scores for the sample averaged M = 220 milliseconds with SS = 6000. Assuming that reaction time for students in the regular population averages μ = 200 milliseconds, are the data sufficient to conclude that the medication has a significant effect on reaction time? Test at the .05 level of significance. Make a point estimate and a 95% confidence interval estimate for the treated population mean.