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Suppose that X1 = Gamma(a= 2, b = 3), X2= Gamma( 3, 3), and X3 =Gamma( 1, 3) are independent. Here B denotes the scale parameter and a denotes the shape parameter. Determine the distribution of Y =
What are the differences between Binomial, hypergiometric, negative geometric, geometric, and poisson. Please provide examples.
If the test statistic for a small sample difference of means test is t* = 2.045, we could reject the Null Hypothesis at alpha = .05 for a two-tailed test with degrees of freedom equal to 16
X1, X2 are random samples of size 3 from a Normal distribution. Use the moment generating function method to prove that the sum Y = X1 + X2 is normally distributed and specify the parameters. Then s
The number of emergency calls received by the local 911 call center is as follows. Using trend projection to forecast the number of calls that will be received during week 11.
The mean length of steel beams manufactured by a properly-working machine is 3.2 meters. An industrial engineer wants to make sure that the machine in not operating incorrectly.
a study compares three levels of Factor A and four levels of Factor B, with seven observations in each cell. What are the degrees of freedom for the F statistic that is used to test for the main eff
Calibrate a regression model of the form of Y = a + b Loge X
Find the minimum sample size when we want to construct a 95% confidence interval on the population proportion for the support of candidate A in the following mayoral election.
Given a sample mean of 27 and a sample standard deviation of 3.5 computed from a sample of size 36, find a 95% confidence interval on the population mean.
A study is conducted to compare mean cholesterol levels for individuals following a low carbohydrate diet for at least 6 months to individuals following a conventional (low fat low calorie) diet for
A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% con
Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation of the sample mean of the time spe
A large university is interested in the outcome of a course standardization process. They have learned that 150 students of the total 1500 students failed to pass the course in the current semester.
What is the expected value for the sampling distribution of the number of school days missed due to influenza?
A bottled water plant utilizes a production process designed to fill bottles with 20 ounces of water. The population of filling volumes is normally distributed with a standard deviation of 1.3 ounce
A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of a
If it appears that the standard deviation is greater, does the new production method appear to be better or worse than the old method? Should the company take any action? -43,79, -22, - 71, -40, 14,
In an analysis investigating the usefulness of pennies, the cents portions of 82 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard d
A simple random sample of pulse rates of 40 women from a normally distributed population results in a standard deviation of 11.2 beats per minute. The normal range of pulse rates of adults is typica
Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 6%. A mutual-fund rating agency randomly selects 29 months and determines
A blackjack consists of two cards, one of which is an Ace and the other of which is a 10-point card, either a 10, Jack, Queen, or King.
The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic.