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
A simple random sample of size n =20 is drawn from a population
that is normally distributed. The sample mean is found to be x = 61
and the sample standard deviation is found to be s =12 Construct a
95% confidence interval about the population mean.
A random sample of size n from a distribution by f(x) = 2x and
F(x) = x^2 ; 0 < x < 1.
Let R = X(n) − X(1) be the range of the sample.
Give a general form of the density function of R
Find P(46≤x¯≤54) for a random sample of size 33 with a mean of
51 and a standard deviation of 10. (Round your
answer to four decimal places.)
True or False: The standard error of the mean, σx¯, is always
larger than the population standard deviation σ.
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%.
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.)...