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2021-02-12
Answered

Whether the provided statement is true or false.

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stuth1

Answered 2021-02-13
Author has **97** answers

Given:

The provided statement is, “As sample size increases, the sampling distribution of \(\overline{x}\) becomes more and more skewed.”

The central limit theorem is one of the important concepts of the large sample theory. It can be stated, “If the size of a sample increases, the population mean can be approximated by the sample mean and the population standard deviation becomes approximately equal to the ratio of the sample standard deviation and the square root of the sample size.”

In other words,central limit theorem, for a sufficiently large sample size, the sampling distributions of the mean tend to be normal distribution, irrespective of the distribution of the population.

Therefore, as sample size increases the sampling distribution of \(\overline{x}\) becomes less and less skewed. Hence, the provided statements are false.

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 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 2021-02-12

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 2021-12-13

Here are summary statistics fro randomly selected weights of newborn girs:

$n=240,\text{}\stackrel{\u2015}{x}=26.1hg,\text{}s=6.3hg$

Construct a confidence interval estimate of the mean. Use a$99\mathrm{\%}$ confidence level. Are these results very different from the confidence interval

$25.1hg<\mu <28.1hg$

with only 13 sample values,

$\stackrel{\u2015}{x}=26.6hg$ and $s=1.8hg?$

What is the confidence interval for the population mean$\mu ?$

Are the results between the two confidence intervals very different?

a) No, because each confidence interval contains the mean of the other confidence interval.

b) No, because the confidence interval limits are similar.

c) Yes, because the confidence interval limits are not similar.

d) Yes, because one confidence interval does not contain the mean of the other confidence interval.

Construct a confidence interval estimate of the mean. Use a

with only 13 sample values,

What is the confidence interval for the population mean

Are the results between the two confidence intervals very different?

a) No, because each confidence interval contains the mean of the other confidence interval.

b) No, because the confidence interval limits are similar.

c) Yes, because the confidence interval limits are not similar.

d) Yes, because one confidence interval does not contain the mean of the other confidence interval.

asked 2022-01-18

What are the mean and standard deviation of a binomial probability distribution with n=12 and $p=\frac{31}{32}$ ?

asked 2020-10-18

How is the distinction between qualitative and quantitative data in social research is essentially the distinction between numerical and nonnumerical data?