Question
In: Math
Suppose that for a dataset the mean is known. Using the 25 random samples, we computed...
Suppose that for a dataset the mean is known. Using the 25
random samples, we computed the sample variance as s^2=0.001.
a) Does the data support the claim that the true standard deviation
is less than 0.05? (use alpha = 0.05 and alternative hypothesis
sigma^2 < 0.0025)
b) Compute a two-sided 95% confidence interval for the true
variance of the data.
Solutions
milcah answered 1 year agoRelated Solutions
Suppose that X and Y are random samples of observations from a population with mean μ...
Suppose that X and Y are random samples of observations from a
population with mean μ and variance σ2.
Consider the following two unbiased point estimators of μ.
A = (7/4)X - (3/4)Y B = (1/3)X +
(2/3)Y
[Give your answers as ratio (eg: as number1 /
number2 ) and DO NOT make any
cancellation]
1. Find variance of A. Var(A) = ?
*σ2
2. Find variance of B. Var(B) = ?
*σ2
3. Efficient and unbiased...
X ~ N (60, 9). Suppose that you form random samples of 25 from this distribution....
X ~
N (60, 9). Suppose that you form
random samples of 25 from this distribution. Let X−be
the random variable of averages. Let
ΣX be the random variable of
sums. To make you easy, drawing the graph, shade the region, label
and scale the horizontal axis for X− and find the
probability.
X−~ N (60, 9/ 25)
9) P (X−< 60) = _____
a. 0.4
b. 0.5
c. 0.6
d. 0.7
10) Find the 30th percentile for the mean.
a. 0.56...
X ~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(70, 11). Suppose that you form random
samples of 25 from this distribution. Let X be the random
variable of averages. Let ΣX be the random variable of
sums.
A. Find the 30th percentile. (Round your answer to two decimal
places.)
B. Sketch the graph, shade the region, label and scale the
horizontal axis for X,and find the probability. (Round your answer
to four decimal places.) P(66 < X < 72) =
C. Sketch the graph, shade the...
X ~ N(50, 11). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(50, 11). Suppose that you form random
samples of 25 from this distribution. Let X be the random variable
of averages. Let ΣX be the random variable of sums.
A. Find the 40th percentile. (Round your answer to two decimal
places.)
B. Sketch the graph, shade the region, label and scale the
horizontal axis for X and find the probability. (Round your answer
to four decimal places.)
P(48 < X < 54) =
C.
Sketch the graph, shade...
X ~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(70, 11). Suppose that you form random
samples of 25 from this distribution. Let X be the random
variable of averages. Let ΣX be the random variable of
sums.
1. Find the 30th percentile. (Round your answer to two decimal
places.)
2. Sketch the graph, shade the region, label and scale the
horizontal axis for X, and find the probability. (Round your answer
to four decimal places.)
P(66 < X < 72) =
3. Sketch the graph, shade...
X ~ N(50, 13). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(50, 13). Suppose that you form random
samples of 25 from this distribution. Let X be the random
variable of averages. Let ΣX be the random variable of
sums.
Part (a)
Sketch the distributions of X and X on the same
graph.
A
B)
C)D)
Part (b)
Give the distribution of X. (Enter an exact number as an
integer, fraction, or decimal.)
X ~ ____(____,____)
Part (c)
Sketch the graph, shade the region, label and scale the horizontal...
X ~ N(60, 12). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(60, 12). Suppose that you form random
samples of 25 from this distribution. Let
X
be the random variable of averages. Let ΣX be the
random variable of sums.
Find the 20th percentile. (Round your answer to two decimal
places.)
X ~ N(70, 14). Suppose that you form random samples of 25 from this distribution. Let...
X ~ N(70, 14). Suppose that you form random samples of 25 from
this distribution. Let X bar be the random variable of averages.
Let ΣX be the random variable of sums. Find the 40th percentile
Suppose we are interested in the mean scores on an exam. A random sample of 36...
Suppose we are interested in the mean scores on an exam.
A random sample of 36 scores is taken and gives a sample mean
(sample mean score) of 68 (x̄ = 68). In this example, we have the
unusual knowledge that the population standard deviation is 3
points. Do not count on knowing the population parameters outside
of textbook examples.
Find a 90% confidence interval for the true (population)
mean of statistics exam scores.
Using a random sample of n = 50, the sample mean is = 13.5. Suppose that...
Using a random sample of n = 50, the sample mean is = 13.5.
Suppose that the population standard deviation is σ=2.5.
Is the above statistical evidence sufficient to make the
following claim μ ≠15:
?o: μ=15
??: μ ≠15
α = 0.05.
p value = 0
Interpret the results using the p value test.
Reject Ho
or
Do not reject Ho
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