If you have a simple random sample of size 300 from a gamma distribution with expected...
If you have a simple random sample of size 300 from a gamma distribution with expected value = 10 and variance 40. What is the probability, approximately, that the sample mean is larger than 9.25?
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If you have a simple random sample of size 300 from a gamma
distribution with expected...
3. Let Xi,... , Xio be a random sample of size 10 from a gamma distribution...
3. Let Xi,... , Xio be a random sample of size 10 from a gamma distribution with α--3 and β 1/e. The prior distribution of θ is a gamma distribution with α-10 and B-2. Recall that the gamma density is given by elsewhere, (a) Find the posterior distribution of θ (b) If we observe 17, use the mean of the posterior distribution to give a point estimate of θ.
A random sample of size n = 25 is obtained from a normally distributed population with...
A random sample of size n = 25 is obtained from a normally distributed population with population mean μ =200 and variance σ^2 = 100. a) What are the mean and standard deviation of the sampling distribution for the sample means? b) What is the probability that the sample mean is greater than 203? c) What is the value of the sample variance such that 5% of the sample variances would be less than this value? d) What is the...
Let Xi,, Xn be a random sample of size n from the normal distribution with mean...
Let Xi,, Xn be a random sample of size n from the normal distribution with mean parameter 0 and variance σ2-3. (a) Justify thatX X, has a normal distribution with mean parameter 0 and variance 3 /n, this is, X~N(0,3/m) (you can do it formally using m.g.f. or use results from normal distribution to justify (b) Find the 0.975 quantile of a standard normal distribution (you can use a table, software or internet to find the quantile). (c) Find the...
Suppose a simple random sample of size n=200 is obtained from a population whose size is...
Suppose a simple random sample of size n=200 is obtained from a population whose size is N= 30,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. A. Not normal because ns0.05N and np(1-P) 10. B. Not normal because ns 0.05N and np(1-p) < 10. C. Approximately normal because ns0.05N and...
Suppose a simple random sample of size n = 75 is obtained from a population whose...
Suppose a simple random sample of size n = 75 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p=0.6. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Not normal because n s 0.05N and np(1-p) < 10. O B. Not normal because ns0.05N and np(1-P) 2 10. O...
Suppose a simple random sample of size 150 is obtained from a population whose size is...
Suppose a simple random sample of size 150 is obtained from a population whose size is N15.000 and whose population proportion with a specified characteristic hp 04. Complete parts () through (c) below. (a) Describe the sampling distribution of Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because 0.05 and 1-10 OB. Approximately normal becausen 00N and re-<10 OG Not normal because 0.06 and 1-12 10 OD. Not normalen SOON and...
A random sample of size 39 is to be selected from a population that has a...
A random sample of size 39 is to be selected from a population that has a mean μ = 53 and a standard deviation σ of 15. (a) This sample of 39 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution. -skewed right -approximately normal -skewed left -chi-square (b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.) (c) Find the standard error of...
7.5 Suppose you draw a random sample of size n from a normal distribution with unknown...
7.5 Suppose you draw a random sample of size n from a normal distribution with unknown mean u and known standard deviation o and construct a 95% confidence interval for u. If you want to halve the margin of error, how much larger would the sample size have to be?
Suppose a simple random sample of size n= 1000 is obtained from a population whose size...
Suppose a simple random sample of size n= 1000 is obtained from a population whose size is N = 2,000,000 and whose population proportion with a specited characteristic is p0.75. Complete parts (a) through (c) below (a) Describe the sampling distribution of O A. Approximately normal, *0.75 and GA 0.0002 OB. Approximately normal pe=0.75 and C 0.0137 O C. Approximately normal. = = 0.75 and 0.0003 P Suppose a simple random sample of strena 1000 is obtained from a population...
3. Let Xi,... , Xio be a random sample of size 10 from a gamma distribution with α--3 and β 1/e. The prior distribution of θ is a gamma distribution with α-10 and B-2. Recall that the gamma density is given by elsewhere, (a) Find the posterior distribution of θ (b) If we observe 17, use the mean of the posterior distribution to give a point estimate of θ.
Let Xi,, Xn be a random sample of size n from the normal distribution with mean parameter 0 and variance σ2-3. (a) Justify thatX X, has a normal distribution with mean parameter 0 and variance 3 /n, this is, X~N(0,3/m) (you can do it formally using m.g.f. or use results from normal distribution to justify (b) Find the 0.975 quantile of a standard normal distribution (you can use a table, software or internet to find the quantile). (c) Find the...
Suppose a simple random sample of size n=200 is obtained from a population whose size is N= 30,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. A. Not normal because ns0.05N and np(1-P) 10. B. Not normal because ns 0.05N and np(1-p) < 10. C. Approximately normal because ns0.05N and...
Suppose a simple random sample of size n = 75 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p=0.6. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Not normal because n s 0.05N and np(1-p) < 10. O B. Not normal because ns0.05N and np(1-P) 2 10. O...
Suppose a simple random sample of size 150 is obtained from a population whose size is N15.000 and whose population proportion with a specified characteristic hp 04. Complete parts () through (c) below. (a) Describe the sampling distribution of Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because 0.05 and 1-10 OB. Approximately normal becausen 00N and re-<10 OG Not normal because 0.06 and 1-12 10 OD. Not normalen SOON and...
7.5 Suppose you draw a random sample of size n from a normal distribution with unknown mean u and known standard deviation o and construct a 95% confidence interval for u. If you want to halve the margin of error, how much larger would the sample size have to be?
Suppose a simple random sample of size n= 1000 is obtained from a population whose size is N = 2,000,000 and whose population proportion with a specited characteristic is p0.75. Complete parts (a) through (c) below (a) Describe the sampling distribution of O A. Approximately normal, *0.75 and GA 0.0002 OB. Approximately normal pe=0.75 and C 0.0137 O C. Approximately normal. = = 0.75 and 0.0003 P Suppose a simple random sample of strena 1000 is obtained from a population...
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