Q1. The sample X = (X,, X2, --, X,) drawn from a Gamma distributed population with parameters a = 3/2 and A. %3D a) Estimate by using Maximum Likelihood Estimation (MLE) method. b) Is the estimator AMLE Consistent? Why? c) Is the estimator AMLE unbiased? Why?

Q: Suppose that a random sample from a normal popula-tion with the known variance σ2 is to be used to…

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Q: Let the mean of the chance sample drawn from a population whose variance is known as 16 and normally…

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Q: In a hypothesis test with hypotheses Ho:u = 90 and H1: 90, a random sample of 16 elements selected…

A:

Q: Let X be a single observation from the Beta (θ,1) population, Let Y = - 1/ln(x). Compute for the…

A: Given: X~Beta (θ,1)Y = - 1/ln(x)Confidence coefficient of the CI (Y/2,Y) for θ=?

Q: Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain…

A: The required probability is calculated as follows:

Q: Let X1,X2, . . . , Xn be a random sample from a gamma distribution withknown parameter α = 3 and…

A: Given,let x1,x2,x3...xn be a random sample fromGamma (α=3,β>0). So, the mean and varianceof the…

Q: To test Ho: o= 2.1 versus H, :0> 2.1, a random sample of size n = 25 is obtained from a population…

A: Given that Sample size n = 25 Sample SD = 2.3 Level of significance = 0.10

Q: Based on these data, can the consumer group conclude, at the 0.05 level of significance, that the…

A: From the provided information, Sample size (n) = 8 Level of significance (α) = 0.05

Q: For a population with phi = 16 , how large a sample is necessary to have a standard error that is…

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Q: The unequal-variances t-test involves a special correction formula for what parameter/s?

A: The unequal variances t test is called the Welch t test.

Q: A simple random sample of sizen= 46 is obtained from a population with u= 64 and o = 17. (a) What…

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Q: A sample of size n = 20 is drawn from a normal population. Find the critical value tα/2 needed to…

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Q: Based on these data, can the consumer group conclude, at the 0.05 level of significance, that the…

A: From the table no.of samples=8 Level of significance=0.05 Now we have to calculate critical value…

Q: A sample of manufactured items will be selected from a large population in which 8 percent of the…

A: Solution: The sampling distribution of the sample proportion to be assumed approximately normal when…

Q: Find the best critical region for testing H : 1 = 2, H:1 = 3 based on the sample drawn from a…

A: Answer: For the given data,

Q: The farmers' association of the Amatole region in the Eastern Cape wants to report on the average…

A: Given that Y1, Y2, Y3, Y4 is a random sample of farms, which is normally distributed with mean μ and…

Q: tion of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that…

A: Given: μ=15, σ=0.5 The critical region is defined as X¯<14.9

Q: A single observation of a random variable havinga geometric distribution is to be used to test the…

A: The random variable X is said to follow geometric distribution if its probability mass function is…

Q: A sample of 900 members has a mean 3.4 cms and S.D. 2.61 cms. Obtain the 95% confidence limits of…

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Q: pothesis test and using either the critical value or p-value approach), and compare your results…

A: 77 50 0 76 69 65 49 62 77 73 57 51 74 67 75 54 56 61 67 62…

Q: In a certain​ survey, 524 people chose to respond to this​ question: "Should passwords be replaced…

A: Given : n = 524 p = 54% = 0.54 q = 1 - p = 0.46 Now, np = 524 × 0.54 = 282.96>= 5 and nq = 524 ×…

Q: If the random sample of X1,…, Xn comes from the uniform (0, Ɵ) distribution, which of the following…

A: Given information: Given that the independent random variables X1, X2, … , Xn are uniformly…

Q: If Y1, Y2, ...,Yn denote a random sample from the normal distribution with mean u and variance o2,…

A: Y1, Y2, Y3,....,Ynare the sample of the normal distribution. The mean of the data is μ. The standard…

Q: Let p, and p, be the respective proportions of women with nutritional anemia in each of two…

A: At 95% confidence level, the z value is 1.96 which can be obtained by using the standard normal…

Q: If X is a Poisson variate with mean 1, show that the standard Poisson variate X-1 is a variable with…

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Q: Suppose small aircraft arrive at a certain airport according to a Poisson process with rate per hour…

A: a. Probability that exactly 6 small aircraft arrive during a 1-hour period: The probability that…

Q: Suppose that a group of researchers is planning to test a new weight loss supplement. They have…

A: It is given that, the population standard deviation is 1.7 and the sample size considered is…

Q: Suppose that the variable under consideration is normally distributed on each of the two populations…

A: Pooled t-procedure and Nonpooled t-procedure is to perform a hypothesis test for the equality of the…

Q: A random sample of size n is to be used to test thenull hypothesis that the parameter θ of an…

A:

Q: Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows:…

A: The given data set is: The level of significance (L) is 0.05. To test the prediction is significant…

Q: Suppose we want to test a hypothesis H,:A=2 vs H :2 =6 by using a random sample of size 30 from a…

A: Given: H0: λ=2 vs H1: λ=6n=30α=0.05

Q: Let X1,X2,.,X, be a random sample from f(x;8) = 0e-nI(0,0)(x). Find a 100y or (1 - a)100 percent…

A: Given that,          Let X1,X2,X3,.....,Xn be a random sample            fx;θ=θe-θxI0,∞(x)…

Q: To test HO: u=50 versus H1: u less than 50, a random sample size of n=25 is obtained from a…

A: From the provided information, Sample size (n) = 25 Sample mean (x̄) = 47.9 Standard deviation (s) =…

Q: A simple random sample of size n= 12 is obtained from a population with u= 63 and o = 14. (a) What…

A: In question,  We have given that a random sample of size n = 12 obtained from a population with mean…

Q: Consider the time series data for the real consumption of hauseholds and government from year 1950…

A: From the given information,   AR(1) AR(2) AR(3) AR(4) AR(5) Intercept 5854.66 5041.07 5365.55…

Q: To test Upper H 0H0​: muμequals=20 versus Upper H 1H1​: muμless than<20​, a simple random sample…

A: Computation of test statistic:In this context, the claim is that the mean is 20 or less. Therefore,…

Q: a) A random sample of 6 insurance claims is selected from a lot of 15 that has 3 non-conforming…

A: NOTE-By bartleby rules, only first question has been answered. As per given by the question, by…

Q: 1,12,.Y, are independent and identically distributed normal random variables with mean u and…

A: Here X ~ N ( μ, σ2) ,  then we have L  = ∏i=1n1σ2πexp-12σ2(xi - μ)2 = 1σ2πn exp -∑i=1n( xi -μ)2/ 2σ2…

Q: 18. Show that for type III population -,0Sx<00, p = 0, e" Tp dp : where p is known, is a maximum…

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Q: Let X1, X2, ..., Xn be a random sample from f(x;0) = 0e-I(0,00)x). Find a 100y or %3D (1– a)100…

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Q: 3. Let X, X2, .. X5, be a random sample from a population having mean u and variance o?, and let ô,…

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Q: Let X1,X2, ...,Xn be a random sample drawn from a N (µ, o2) distribution, where known and o2 is…

A: Introduction: An estimator is said to be a consistent estimator for a parameter, if it converges in…

Q: 6. Using the Neymann-Pearson lemma, develop the best test to test Ho: =10 versus Ha: H = 11 based on…

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Q: Let X1, X2,......, X, be a random sample from a normal population N(u, o2) EXi is a ΣΧ. , show that…

A: Given X1, X2, ..., Xn be a random sample from a normal population Nμ, σ2.

Q: Let X be the life in hours of a radio tube. Assume that X is normally distributed with the mean 200…

A: It is given that the life in hours of a radio tube is normally distributed with the mean 200 and…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.