Let ?1,?2, ?3, … , ?25, be a random sample from a normal distribution having variance...

Let ?1,?2, ?3, … , ?25, be a random sample from a normal distribution having variance 100.

a. Find the rejection region for a test at level ? = .1 of ?0: ? = 0 ?1: ? = 1.5

b. What is the power of the test?

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orchestra answered 2 years ago

Let X have Normal distribution with mean 45 and variance 81. If a random sample of...

Let X have Normal distribution with mean 45 and variance 81. If a random sample of size 25 is taken, which of the following is the probability that the sample average is between 41.40 and 45.63?

a. A random sample of 25 is taken from a normal distribution with population mean =...

a. A random sample of 25 is taken from a normal distribution with population mean = 62, and population standard deviation = 7. What is the margin of error for a 90% confidence interval? b. Repeat the last problem if the standard deviation is unknown, given that the sample standard deviation is S=5.4

2. Let X be a normal random variance with media 1 and variance 4. Consider a...

2. Let X be a normal random variance with media 1 and variance 4. Consider a new variance A random variable T defined below: T = -1 if X < -2 T = 0 if - 2 ≤ X ≤ 0 T = 1 if x>0 Find the moment generating function of T and, from it, calculate E (T) and Var (T).

2. Let X be a normal random variance with media 1 and variance 4. Consider a...

2. Let X be a normal random variance with media 1 and variance 4. Consider a new variance A random variable T defined below: T = -1 if X < -2 T = 0 if - 2 ≤ X ≤ 0 T = 1 if x>0 Find the moment generating function of T and, from it, calculate E (T) and Var (T).

2. Let X1, . . . , Xn be a random sample from the distribution with...

2. Let X1, . . . , Xn be a random sample from the distribution with pdf given by fX(x;β) = β 1(x ≥ 1). xβ+1 (a) Show that T = ni=1 log Xi is a sufficient statistic for β. Hint: Use n1n1n=exp log=exp −logxi .i=1 xi i=1 xi i=1 (b) Find the pdf of Y = logX, where X ∼ fX(x;β). (c) Find the distribution of T . Hint: Identify the distribution of Y and use mgfs. (d) Find...

Let z denote a random variable having a normal distribution with ? = 0 and ?...

Let z denote a random variable having a normal distribution with ? = 0 and ? = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.3) = (b) P(z < -0.3) = (c) P(0.40 < z < 0.85) = (d) P(-0.85 < z < -0.40) = (e) P(-0.40 < z < 0.85) = (f) P(z > -1.26) = (g) P(z < -1.5 or z > 2.50) =

Question #3. A random sample of n = 9 is selected from a normal distribution with...

Question #3. A random sample of n = 9 is selected from a normal distribution with μ = 80 and σ=12. What is the probability that the sample mean will be between 75 and 86? Report to the thousandths Question #4. A random sample of n= 4 is obtained from a normal distribution μ= 30,σ= 8. What is the probability the sample mean will be smaller than M = 22? Report to the thousandths Question #5. A random sample of...

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Let ?1,?2, ?3, … , ?25, be a random sample from a normal distribution having variance...

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