Question

In: Statistics and Probability

(a) Generate n=10 random sample from a population with normal(40,1) distribution. (b) For data in part...

(a) Generate n=10 random sample from a population with normal(40,1) distribution.

(b) For data in part (a) find a 95% confidence interval for mu (the mean of the population). Can I claim that the mean is 41? If your answer is "yes" to this question, which one is the mean? 40 or 41?

(c) For data in part (a) find a 99% confidence interval for sigma (the standard deviation of the population).

Expert Solution

(a)

> set.seed(1)
> rnorm(10,40,1)
[1] 39.37355 40.18364 39.16437 41.59528 40.32951 39.17953 40.48743 40.73832 40.57578 39.69461

(b)

For the data at hand,

So,

Then, % confidence interval for mean is given by--

So, at 95% confidence on the basis of the data, it would be an exaggeration t say the mean is 41. The mean can well be 40 as it lies withing our 95% confidence interval.

(c)

Here we are to find 99% confidence interval for sigma.

% confidence interval for mean is given by--

orchestra answered 2 years ago

A random sample of n = 7 observations from a normal distribution resulted in the data...

A random sample of n = 7 observations from a normal distribution resulted in the data shown in the table. Compute a 90% confidence interval for sigma squared. 91 99 106 95 84 69 84

a. A random sample of 25 is taken from a normal distribution with population mean =...

a. A random sample of 25 is taken from a normal distribution with population mean = 62, and population standard deviation = 7. What is the margin of error for a 90% confidence interval? b. Repeat the last problem if the standard deviation is unknown, given that the sample standard deviation is S=5.4

A random sample of n = 100 scores is selected from a normal population with a...

A random sample of n = 100 scores is selected from a normal population with a mean of μ = 60 and a standard deviation of σ = 20. What is the probability of obtaining a sample mean greater than M = 57?

Assuming the population has an approximate normal distribution, if a sample size n=10 has a sample...

Assuming the population has an approximate normal distribution, if a sample size n=10 has a sample mean ¯x=36 with a sample standard deviation s=9, find the margin of error at a 90% confidence level. THEN YOU MUST ROUND ANSWER TO TWO DECIMALS PLACES.

A sample of size n = 10 n=10 is drawn from a population. The data is...

A sample of size n = 10 n=10 is drawn from a population. The data is shown below. 98.8 110.5 117.2 100.2 135.2 135.2 135.2 115.8 125.8 106.6 What is the range of this data set? range = What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, reporting 2 more decimal places than the original data. Please, please, please do not calculate the value by hand. stdev =

A sample of n = 9 scores is obtained from a normal population distribution with σ...

A sample of n = 9 scores is obtained from a normal population distribution with σ = 12. The sample mean is M = 60. a. With a two-tailed test and α = .05, use the sample data to test the hypothesis that the population mean is μ = 65. b. With a two-tailed test and α = .05, use the sample data to test the hypothesis that the population mean is μ = 55. c. In parts (a) and...

7.A random sample of 49 observations is drawn from a population with a normal distribution. If...

7.A random sample of 49 observations is drawn from a population with a normal distribution. If the sample mean is 265 and the sample standard deviation is 57, find the 95% confidence interval for the population mean. 8. A random sample of 49 observations is drawn from a population with a normal distribution with a standard deviation of 57. If the sample mean is 265, find the 95% confidence interval for the population mean. Compare this confidence interval with the...

Question #3. A random sample of n = 9 is selected from a normal distribution with...

Question #3. A random sample of n = 9 is selected from a normal distribution with μ = 80 and σ=12. What is the probability that the sample mean will be between 75 and 86? Report to the thousandths Question #4. A random sample of n= 4 is obtained from a normal distribution μ= 30,σ= 8. What is the probability the sample mean will be smaller than M = 22? Report to the thousandths Question #5. A random sample of...

A random sample of n =100 is selected from a normal population with mean μ =...

A random sample of n =100 is selected from a normal population with mean μ = 24 and standard deviation σ = 1.25. Find the probability that is less than 24.3

A simple random sample from a population with a normal distribution of 108 body temperatures has...

A simple random sample from a population with a normal distribution of 108 body temperatures has x = 98.30 degrees F° and s = 0.68 degrees F° Construct a 95% confidence interval estimate of the standard deviation of body temperature of all healthy humans. (Round to two decimal places as needed.)