2) Explain The Central Limit Theorem

3) Explain how confidence intervals are created and what can they tell us about population parameters

FobelloE
2021-03-11
Answered

1) Describe sampling distributions and sampling variavility

2) Explain The Central Limit Theorem

3) Explain how confidence intervals are created and what can they tell us about population parameters

2) Explain The Central Limit Theorem

3) Explain how confidence intervals are created and what can they tell us about population parameters

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Leonard Stokes

Answered 2021-03-12
Author has **98** answers

Step 1

1)

The sampling distributions refers to the probability distributions of all possible values of the sample statistic for example, sample mean.

The sampling variability tells us how an estimate varies between different samples. It is often measured in terms of variance or standard deviation. There are three factors involved in variability,

The size of the population

The size of the sample

The sampling method (with or without replacement)

Step 2

2)

The central limit theorem tells us that in a random sample of size n taken from a population, its sampling distribution can be approximated to a normal distribution by taking a larger sample size. That is, whatever might be the population distribution, the sampling distribution of a sample statistic can be approximated to normal by increasing the sample size.

Step 3

3)

The confidence interval are created using the sample statistic and the margin of error.

$CI=\stackrel{\u2015}{x}\pm {Z}_{\frac{\alpha}{2}}(\frac{\sigma}{\sqrt{n}}n)$

$=\stackrel{\u2015}{x}\pm ME$

${Z}_{\frac{\alpha}{2}}$ represents the critical value of the normal distribution and this distribution is used if the population standard deviation is known. For unknown population standard deviation, the sample standard deviation is used with student’s t distribution.

The constructed confidence interval with say 95 or 90 percent confidence level tells us that if repeated samples were to be taken and confidence intervals were to be built, then 95 or 90 percent of these constructed confidence intervals would contain the true value of the parameter (mean).

1)

The sampling distributions refers to the probability distributions of all possible values of the sample statistic for example, sample mean.

The sampling variability tells us how an estimate varies between different samples. It is often measured in terms of variance or standard deviation. There are three factors involved in variability,

The size of the population

The size of the sample

The sampling method (with or without replacement)

Step 2

2)

The central limit theorem tells us that in a random sample of size n taken from a population, its sampling distribution can be approximated to a normal distribution by taking a larger sample size. That is, whatever might be the population distribution, the sampling distribution of a sample statistic can be approximated to normal by increasing the sample size.

Step 3

3)

The confidence interval are created using the sample statistic and the margin of error.

The constructed confidence interval with say 95 or 90 percent confidence level tells us that if repeated samples were to be taken and confidence intervals were to be built, then 95 or 90 percent of these constructed confidence intervals would contain the true value of the parameter (mean).

asked 2020-12-07

Which of the following are possible examples of sampling distributions? (Select all that apply.)

mean trout lengths based on samples of size 5

average SAT score of a sample of high school students

average male height based on samples of size 30

heights of college students at a sampled universit

yall mean trout lengths in a sampled lake

mean trout lengths based on samples of size 5

average SAT score of a sample of high school students

average male height based on samples of size 30

heights of college students at a sampled universit

yall mean trout lengths in a sampled lake

asked 2021-03-04

Which of the following statements about the sampling distribution of the sample mean is incorrect?

(a) The standard deviation of the sampling distribution will decrease as the sample size increases.

(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.

(c) The sample mean is an unbiased estimator of the population mean.

(d) The sampling distribution shows how the sample mean will vary in repeated samples.

(e) The sampling distribution shows how the sample was distributed around the sample mean.

(a) The standard deviation of the sampling distribution will decrease as the sample size increases.

(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.

(c) The sample mean is an unbiased estimator of the population mean.

(d) The sampling distribution shows how the sample mean will vary in repeated samples.

(e) The sampling distribution shows how the sample was distributed around the sample mean.

asked 2021-03-09

Which of the following is true about the sampling distribution of means?

A. Shape of the sampling distribution of means is always the same shape as the population distribution, no matter what the sample size is.

B. Sampling distributions of means are always nearly normal.

C. Sampling distributions of means get closer to normality as the sample size increases.

D. Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.

A. Shape of the sampling distribution of means is always the same shape as the population distribution, no matter what the sample size is.

B. Sampling distributions of means are always nearly normal.

C. Sampling distributions of means get closer to normality as the sample size increases.

D. Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.

asked 2021-02-12

Which of the following is true about sampling distributions?

-Shape of the sampling distribution is always the same shape as the population distribution, no matter what the sample size is.

-Sampling distributions are always nearly normal.

-Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.

-Sampling distributions get closer to normality as the sample size increases.

-Shape of the sampling distribution is always the same shape as the population distribution, no matter what the sample size is.

-Sampling distributions are always nearly normal.

-Sampling distribution of the mean is always right skewed since means cannot be smaller than 0.

-Sampling distributions get closer to normality as the sample size increases.

asked 2020-11-11

Explain how to use the sampling distributions of A and B to decide which is the best estimator of $\alpha $ .

asked 2020-10-20

Check whether the standard error of the sampling distributions of bar p obtained in part(a) and part(b) are different.

asked 2021-06-26