A random sample of size n = 2 is chosen without replacement from
the set{ 1 , 2 , 3 } . X = 0 if the first number is even, and X = 1
if the first number is odd. Y = 0 if the second number is even, and
Y = 1 if the second number is odd.
a) List all of the samples.
(b) Find the joint distribution of X and Y.
(c) Are X and Y...
For a data set obtained from a sample of size n = 121
with x- = 44.25, it is known that σ = 5.4.
(a) What is the point estimate of
µ?
(b) Find z score corresponding to a 95%
confidence level, zα/2. Recall that
(1 − α)100% = 95%.
(c) Construct a 95% confidence interval for
µ.
(d) What is the margin of error in part
(c)?
How many arrangements of length n where 1 ≤ n ≤ 8 can be formed
from the letters A, A, B, C, C, C, D, E where
(a) both A’s are adjacent?
(b) the string starts or ends with A?
(c) you use (exactly) 4 letters from the list?
Let f(n,k) be the number of equivalence relations with k classes
on set with n elements.
a) What is f(2,4)?
b) what is f(4,2)?
c) Give a combinational proof that f(n,k) = f(n-1,k-1)+k *
f(n-1,k)
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.)...