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You own a store that sells light bulbs. Customers have been complaining that the bulbs you sell burn out quickly. You want to identify which of two factories (Factory A or Factory B) is the one producing the current batch of light bulbs in your store. You have n light bulbs in your test batch, but you do not know from which factory these bulbs came. Furthermore, you have no a priori reason to think one factory is more likely than the other. You have examined m light bulbs (where m < n) and you have measured the lifetime of these m light bulbs.
Assume that the light bulbs produced in Factory A have a lifetime you can model as being exponentially distributed with parameter A. Assume that the light bulbs produced in Factory B have a lifetime you can model as being exponentially distributed with parameter B. Finally, assume that the lifetimes of the light bulbs are conditionally independent given the parameters.Let be the exponential failure rate for light bulbs in your test batch of size n.(a) Assuming that you know A and B, write the posterior probability distribution of .(b) Assume the following independent prior distributions for A and B:AjA; A Gamma(A; A)BjB; B Gamma(B; B)The posterior distribution of with these assumptions. What is the name of this type of distribution?
A nurse at a local hospital is estimating the weight of infants. how large a sample must she select if she desires to be 95% confident that the true mean is within 3 ounces of the sample mean?
If you wish to estimate a population mean with a sampling distribution error SE = 0.28 using a 95% confidence interval and you know from prior sampling that sigma^2 is approximately equal to 5.4, how many observations would have to be included in ..
A sample of 148 of our statistics students rated their level of admiration for Hilary Rodham Clinton on a scale of 1 to 7. The mean rating was 4.06 and the standard deviation was 1.70.
If you were to draw a scatter plot of the number of women in the workforce versus the number of Christmas trees sold in the United States for each year between 1930 and the present
A college would like to have an entering class of 1200 students. Because not all students who are offered admission accept, the college admits more than 1200 students.
Find the margin of error for a 89% confidence interval for the true mean cost of textbooks of U of M students in one semester.
The weight of an almond is normally distributed with mean 0.05 ounce and standard deviation of 0.015 ounce. Find the probability that a package of 100 almonds will weigh between 4.3 and 5.3 ounces.
A rectangular garden has dimensions of 25 feet by 19 feet . A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 672 square feet?
An element E has a constant failure rate (lamda) and a reliability at time t of R(t)=p, if p=0.2 and 0.8, What is the effect on Rs(t), and basic reliability, serial MTBF, of adding additional elements to the series baseline system containing a sin..
Correlation between the two variables - Evaluate the value of the correlation coefficient.
Explain the difference between testing a single mean and testing the difference between two means. What two assumptions must be met when one is using z test to test differences between two means?
To guarantee that cans of soda are properly filled, some cans are sampled and the amounts measured. The overall average for the samples is 12 ounces.
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