Consider a random sample of size n from a distribution with
function F (X) = 1- x-2 if x > 1 and zero elsewhere.
Determine if each of the following sequences has distribution
limit; if so, give the limit distribution.
a)x1:n
b)xn:n
c)n-1/2 xn:n
Let X be the mean of a random sample of size n from a N(μ,9)
distribution.
a. Find n so that X −1< μ < X +1 is a confidence interval
estimate of μ with a confidence level of at least 90%.
b.Find n so that X−e < μ < X+e is a confidence interval
estimate of μ withaconfidence levelofatleast (1−α)⋅100%.
Q1: If X~(42,10) and is computed from a random sample
of size n=81, what is the distribution of ?
Q2: If X~N(42,10) and is computed from a random
sample of size n=16, what is the distribution of ?
Q3: When constructing a confidence interval for a mean, what are
the two fundamentally different scenarios we would be working
under?
Q4: Interpret the following probability statement into a
complete sentence: P(x-bar > 20.26) = 0.8084
Q5: Find the following probability: P( Z > 0).
Given a random sample of size of n = 4,900 from a binomial
probability distribution with P = 0.50, complete parts (a)
through (e) below.
a. Find the probability that the number of successes is greater
than 2,535.
P(X>2535) =
b. Find the probability that the number of successes is fewer
than 2,410.
P(X<2410) =
c. Find the probability that the number of successes is between
2,440 and 2,520.
P(2440 < X < 2520) =
d. With probability .20, the...
A random sample of size n = 100 is taken from a population of
size N = 600 with a population proportion of p =0.46. Is it
necessary to apply the finite population correction factor?
Calculate the expected value and standard error of the sample
proportion. What is the probability that the sample mean is less
than .40?
A random sample of size n = 69 is taken from a
population of size N = 971 with a population proportion
p = 0.68.
a-1. Is it necessary to apply the finite
population correction factor?
Yes or no?
a-2. Calculate the expected value and the
standard error of the sample proportion. (Round "expected
value" to 2 decimal places and "standard error" to 4 decimal
places.)
Expected Value-
Standard Error-
b. What is the probability that the sample
proportion is...
A random sample of size n = 71 is taken from a population of
size N = 639 with a population proportion p = 0.73.
a-1. Is it necessary to apply the finite
population correction factor?
a-2. Calculate the expected value and the
standard error of the sample proportion. (Round "expected
value" to 2 decimal places and "standard error" to 4 decimal
places.)
b. What is the probability that the sample
proportion is less than 0.66? (Round “z” value to...
A random sample of size n = 152 is taken from a
population of size N = 3,300 with mean μ = −71
and variance σ2 = 112. [You may find it
useful to reference the z table.]
a-1. Is it necessary to apply the finite
population correction factor?
Yes
No
a-2. Calculate the expected value and the standard
error of the sample mean. (Negative values should be
indicated by a minus sign. Round "standard error" to 2
decimal places.)...
A random sample of size n = 472 is taken from a population of
size N = 9,700 with mean μ = −63 and variance σ2 = 176. [You may
find it useful to reference the z table.]
A-1
Is it necessary to apply the finite population correction
factor?
Yes
No
a-2. Calculate the expected value and the
standard error of the sample mean. (Negative values should
be indicated by a minus sign. Round "standard error" to 2
decimal places.)...
Dr. Lee now wants to generate a random sample of size 10,000
from the F distribution with df1 = 1 and df2 = 4 degrees of
freedom. But he doesn’t remember the probability density function
(pdf) of the F distribution at all. Fortunately, he knows the
relationship between t distribution and F distribution. He knows
that if X follows the t distribution with ν = 4 degrees of freedom,
then X2 follows the F distribution with df1 = 1 and...