Question
In: Statistics and Probability
Let X be the mean of a random sample of size n from a N(μ,9) distribution....
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%.
Solutions
orchestra answered 2 years agoRelated Solutions
Let X ∼ N(µ, σ) and X¯ be sample mean from a random sample of 9....
Let X ∼ N(µ, σ) and X¯ be sample mean from a random sample of
9.
Suppose you draw a random sample of 9, calculate an interval ¯x
± 0.5σ where σ is the population standard deviation of X, and then
check whether µ, the population mean, is contained in the interval
or not.
If you repeat this process 100 times, about how many time do you
think µ is contained in X¯ ± 0.5σ. Explain why. (Hint: What is...
A sample of size n = 16 is made from a normal distribution with mean μ....
A sample of size n = 16 is made from a normal distribution with
mean μ. It
turns out that the sample mean is x = 23 and the sample standard
deviation is s = 6.
Construct a 90% confidence interval for μ.
A random sample of size n = 55 is taken from a population with mean μ...
A random sample of size n = 55 is taken from a
population with mean μ = −10.5 and standard deviation
σ = 2. [You may find it useful to reference
the z table.]
a. Calculate the expected value and the
standard error for the sampling distribution of the sample mean.
(Negative values should be indicated by a minus sign. Round
"expected value" to 1 decimal place and "standard error" to 4
decimal places.)
b. What is the probability that...
A random sample of size n = 50 is taken from a population with mean μ...
A random sample of size n = 50 is taken from a
population with mean μ = −9.5 and standard deviation
σ = 2. [You may find it useful to reference
the z table.]
a. Calculate the expected value and the
standard error for the sampling distribution of the sample mean.
(Negative values should be indicated by a minus sign.
Round "expected value" to 1 decimal place and
"standard deviation" to 4 decimal places.)
Expected Value=
Standard Error=
b. What...
A random sample of size n from a distribution by f(x) = 2x and F(x) =...
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
Let the random variable X follow a normal distribution with a mean of μ and a...
Let the random variable X follow a normal distribution with a
mean of μ and a standard deviation of σ. Let 1 be the mean of a
sample of 36 observations randomly chosen from this population, and
2 be the mean of a sample of 25 observations randomly chosen from
the same population.
a) How are 1 and 2 distributed? Write down the form of the density
function and the corresponding parameters.
b) Evaluate the statement:
?(?−0.2?< ?̅1 < ?+0.2?)<?(?−0.2?<...
Consider a random sample of size n from a distribution with function F (X) = 1-...
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 is drawn. The sample mean, x overbar x, is...
A simple random sample of size n is drawn. The sample mean, x
overbar x, is found to be 17.8, and the sample standard
deviation, s, is found to be 4.9.
(a) Construct a 95% confidence interval about mu μ if the
sample size, n, is 34.
Lower bound=
Upper bound=
(Use ascending order. Round to two decimal places as
needed.)
(b) Construct a 95% confidence interval about mu μ if the
sample size, n, is 61.
Lower bound=
Upper...
A simple random sample of size n is drawn. The sample mean, x, is found to...
A simple random sample of size n is drawn. The sample mean, x,
is found to be 18.5, and the sample standard deviation, s, is
found to be 4.6.
(a) Construct a 95% confidence interval about μ if the sample
size, n, is 34.
Lower bound: ___
Upper bound: ___
(Use ascending order. Round to two decimal places as
needed.)
(b) Construct a 95% confidence interval about μ if the sample
size, n, is 61.
Lower bound: ___
Upper bound:...
A simple random sample of size n is drawn. The sample mean, x, is found to...
A simple random sample of size n is drawn. The sample
mean, x, is found to be 35.1, and the sample standard deviation, s,
is found to be 8.7
a) Construct a 90% confidence interval for μ if the
sample size, n, is 100.
b) Construct a 90% confidence interval for μ if the
sample size, n, is 40. How does decreasing the sample size affect
the margin of error, E?
c) Construct a 96% confidence interval for μ if...
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