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

Expert Solution


Related 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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT