Question
In: Statistics and Probability
We have two normal populations with unknown means μ₁ and μ₂ and a common variance σ²....
We have two normal populations with unknown means μ₁ and μ₂ and a common variance σ². Two independent samples are randomly drawn from the populations with the following data:
n₁ = 26 xത₁ = 8.35 s₁ = 1.7
n₂ = 34 xത₂ = 7.46 s₂ = 2.2
(a)[5] At the level of significance α = 0.01, test H₀: μ₁ = μ₂ versus H₁: μ₁ ≠ μ₂. Sketch the test.
(b)[2] Sketch and find the p‐value of the test in part (a). Would you reject H₀ if α = 0.10?
(c)[3] Construct the 99% CI for the sample mean difference (xത₁ ‐ xത₂). Based on the CI, can the two means be the same? Do you see the conclusion similarity between part (a) and part (c)? Hint: Use 5 decimal places. Use some Excel lookups for values and probabilities.
Solutions
Expert Solution
NOW , P VALUE CAN BE CALCULATED THROUGH V LOOK UP IN EXCEL BY THE FUNCTION, tdist(t,degree_of_freedom,tails) .
I HOPE I WAS HELPFUL AND HAVE CLEARED YOUR DOUBTS.
THANKYOU
orchestra answered 1 year agoRelated Solutions
We have two normal populations with unknown means μ₁ and μ₂ and a common variance σ²....
We have two normal populations with unknown means μ₁ and μ₂ and
a common variance σ². Two independent samples are randomly drawn
from the populations with the following data: n₁ = 26
xത₁ = 8.35 s₁ = 1.7 n₂ = 34 xത₂ = 7.46 s₂ = 2.2
(a)[5] At the level of significance α = 0.01, test H₀: μ₁ = μ₂
versus H₁: μ₁ ≠ μ₂. Sketch the test.
(b)[2] Sketch and find the p‐value of the test in part...
You have a normal population of scores with μ = 50 and σ = 14. We...
You have a normal population of scores with μ = 50 and σ = 14.
We obtain a random sample of n = 36. What is the
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We have a normal probability distribution for variable x with μ = 24.8 and σ =...
We have a normal probability distribution for variable x with μ
= 24.8 and σ = 3.7. For each of the following, make a pencil sketch
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(a)[1] PDF(x = 30); [use NORM.DIST(•,•,•,0)]
(b)[1] P(x ≤ 27); [use NORM.DIST(•,•,•,1)]
(c)[1] P(x ≥ 21); [elaborate, then use
NORM.DIST(•,•,•,1)]
(d)[2] P(22 ≤ x ≤ 26); [elaborate, then use
NORM.DIST(•,•,•,1)]
(e)[3] P(20 ≤ x ≤ 28); [z‐scores, then use
NORM.S.DIST(•,1)]
(f)[1] x* so that...
A. A normal random variable has an unknown mean μ and a standard deviation σ =...
A. A normal random variable has an unknown mean μ and a standard
deviation σ = 2. If the probability that x exceeds 6.5 is .9732;
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C. A standard normal random variable has μ = 0 and a standard
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D. A standard normal random...
1) A normal random variable x has an unknown mean μ and standard deviation σ =...
1) A normal random variable x has an unknown mean
μ and standard deviation σ = 2. If the
probability that x exceeds 4.6 is 0.8023, find μ.
(Round your answer to one decimal place.)
μ =
2) Answer the question for a normal random variable x
with mean μ and standard deviation σ specified
below. (Round your answer to four decimal places.)
μ = 1.3 and σ = 0.19.
Find
P(1.50 < x <
1.71).
P(1.50 < x <...
1. Suppose X follows the normal distribution with mean μ and variance σ^2 . Then: (Circle...
1. Suppose X follows the normal distribution with mean μ and
variance σ^2 . Then:
(Circle all that apply.)
A. X is symmetric with respect to the y-axis.
B. P(X=2)=P(X=-2).
C. Y=aX follows the same distribution as X, where a is a
constant.
D. None of the above statements is correct.
2.
Given a random variable X having a normal distribution with
μ=50, and σ=10. The probability that Z assumes a value between 45
and 62 is: ___________.
3. Which...
For normal data with unknown mean µ and σ^2, we use the prior f (µ, log(σ))...
For normal data with unknown mean µ and σ^2, we use the prior f
(µ, log(σ)) = 1.
23 data points: 5.36 5.29 5.58 5.65 5.57 5.53 5.62 5.29 5.44
5.34 5.79 5.1 5.27 5.39 5.42 5.47 5.63 5.34 5.46 5.3 5.75 5.68
5.85
Q. Draw sample (or theoretical) posterior joint pdf of (µ, σ^2),
marginal pdf of µ, marginal pdf of σ^2, and posterior predictive
pdf.
Perform a hypothesis test (comparing means) on the two populations below. Assume equal means and normal...
Perform a hypothesis test (comparing means) on the two
populations below. Assume equal means and normal distribution.
Population A
Population B
42
65
41
22
50
51
25
17
78
24
35
57
19
67
22
26
45
88
45
85
For a normal distribution with a mean of μ = 150 and an SD of σ...
For a normal distribution with a mean of μ = 150 and an SD of σ
= 15:
3. Find these probabilities: a. p (X > 150)
b. p(X < 120)
c. p(X < 170)
d. p(130 < X < 175)
Let X1,...,Xn be iid N(μ , σ^2) with μ known and σ^2 unknown. Please carefully re-read...
Let X1,...,Xn be iid N(μ , σ^2) with μ known and σ^2 unknown.
Please carefully re-read that sentence, as it is an uncommon
setup!
(a) Find the Cramer-Rao lower bound for an unbiased estimator of
σ^2.
(b) The MLE for σ^2 is ∑(xi−μ)^2 / n. Find the variance of this
estimator. You may find use of the following property: E[(X−μ)^4] =
3σ^4.
c) Find the efficiency of the MLE. Is it a MVUE? Explain.
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