Question
In: Statistics and Probability
Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to...
Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to test H0: μ=10 versus H1: μ=10. The sample moments are x ̄ = 13.4508 and s2 = 65.8016. (a) Find the critical region C and test the null hypothesis at the 5% level. What is your decision? (b) What is the p-value for your decision? (c) What is a 95% confidence interval for μ?
Solutions
orchestra answered 2 years agoRelated Solutions
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...
We have a random sample of size n (which is large), and we wish to test...
We have a random sample of size n (which is large), and we wish
to test - Ho: X~UNIF(0,1) vs Ha: X~exp(1). How would you conduct
hypothesis testing? Describe procedure.
Suppose X1, . . . , Xn is a random sample from the Normal(μ, σ2) distribution,...
Suppose X1, . . . , Xn is a random sample from the Normal(μ, σ2)
distribution, where μ is unknown but σ2 is known, and it is of
interest to test H0: μ = μ0 versus H1: μ ̸= μ0 for some value μ0.
The R code below plots the power curve of the test
Reject H0 iff |√n(X ̄n − μ0)/σ| > zα/2
for user-selected values of μ0, n, σ, and α. For a sequence of
values of μ,...
What is the minimum sample size required for estimating μ for N(μ, σ2=121) to within ±...
What is the minimum sample size required for estimating μ for
N(μ, σ2=121) to within ± 2 with confidence levels 95%,
90%, and 80%?
a. Find the minimum sample size for the 95%
confidence level. Enter an integer below. You must round up.
b. Find the minimum sample size for the 90%
confidence level.
c. Find the minimum sample size for the 80%
confidence level.
We have a random sample of size 10 from a normal distribution. We wish to estimate...
We have a random sample of size 10 from a normal distribution.
We wish to estimate the population mean. Damjan suggests taking the
average of the sample minimum and sample maximum. Allan thinks this
will be a poor estimator and says we should use the sample mean
instead. Do a simulation in R to compare these two
estimators in terms of their bias and variance. Include a
side-by-side boxplot that compares their sampling
distributions.
We have a random sample of size 10 from a normal distribution. We wish to estimate...
We have a random sample of size 10 from a normal distribution.
We wish to estimate the population mean. joseph suggests taking the
average of the sample minimum and sample maximum.steve thinks this
will be a poor estimator and says we should use the sample mean
instead. Do a simulation in R to compare these two estimators in
terms of their bias and variance. Include a side-by-side boxplot
that compares their sampling distribut
showing R output also
Suppose a simple random sample of size n=64 is obtained from a population with μ=76 and...
Suppose a simple random sample of size n=64 is obtained from a
population with μ=76 and σ=8.
(a) Describe the sampling distribution of x̅
(b) What is P (x̅ > 77.7)?
(c) What is P (x̅ ≤ 73.65)?
(d) What is P (74.5 < x̅ < 78.15)?
26-Suppose a simple random sample of size n=36 is obtained from a population with μ=64 and...
26-Suppose a simple random sample of size n=36 is obtained from
a population with μ=64 and σ=15.
1- P(x->65.5) =
2- P(x->c) = 0.72. Find c.=
3- P(64.3<x-<65.65) =
4-P(|z|<c) = 0.45, Find c.=
5-P(|z|>c) = 0.35. Find c.=
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 simple random sample of size n = 15 is obtained from a population with μ...
A simple random sample of size n = 15 is obtained from a
population with μ = 97 and σ = 23. Enter your answer as an area
under the curve with 4 decimal places. P(x⎯⎯⎯ ≤ 94)
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