Question

Indicate whether the following statements are true or false. If we took a random sample of 35 subjects from some population, the associated sampling distribution of the mean would have the following properties: - Shape would approximate a normal curve. - Mean would equal the one sample mean. - Shape would approximate the shape of the population. - Compared to the population variability, the variability would be reduced by a factor equal to the square root of 35. - Mean would equal the population mean. - Variability would equal the population variability. Given a sample size of 36, how large does the population standard deviation have to be in order for the standard error to be: Standard Error = SD/(√Sample Size) (a) 1: standard deviation (b) 2: standard deviation (c) 5: standard deviation (d) 100: standard deviation

          Indicate whether the following statements are true or false. If we took a random sample of 35 subjects from some population, the associated sampling distribution of the mean would have the following properties: 
- Shape would approximate a normal curve.
- Mean would equal the one sample mean.
- Shape would approximate the shape of the population.
- Compared to the population variability, the variability would be reduced by a factor equal to the square root of 35.
- Mean would equal the population mean.
- Variability would equal the population variability.

Given a sample size of 36, how large does the population standard deviation have to be in order for the standard error to be:
Standard Error = SD/(√Sample Size)
(a) 1: standard deviation
(b) 2: standard deviation
(c) 5: standard deviation
(d) 100: standard deviation

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Added by Daniela H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Lucas Finney

07/18/2022

Step 1

Step 1: The first statement is true, as with a sample size of 35, the sampling distribution of the mean would approximate a normal curve due to the central limit theorem. Show more…

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Indicate whether the following statements are true or false. If we took a random sample of 35 subjects from some population, the associated sampling distribution of the mean would have the following properties: - Shape would approximate a normal curve. - Mean would equal the one sample mean. - Shape would approximate the shape of the population. - Compared to the population variability, the variability would be reduced by a factor equal to the square root of 35. - Mean would equal the population mean. - Variability would equal the population variability. Given a sample size of 36, how large does the population standard deviation have to be in order for the standard error to be: Standard Error = SD/(√Sample Size) (a) 1: standard deviation (b) 2: standard deviation (c) 5: standard deviation (d) 100: standard deviation

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00:01 For this problem, we are asked to indicate whether the following statements are true or false.

00:05 If we took a random sample of 35 subjects from some population, the associated sampling distribution of the mean would have the following properties.

00:13 So first statement, shape would approximate a normal curve.

00:16 So this statement here, that first one, is true.

00:20 That's because of the fact that with a sample size of 35, that is sufficiently large that the central limit theorem would apply, the sampling distribution would approximate the normal curve.

00:30 The mean would equal the one sample mean.

00:35 So in this case, yes.

00:37 So the, actually, i'm going to be careful with interpreting this.

00:43 I would say, okay, well, we take a, we're taking a single random sample of 35 subjects.

00:52 Okay, and then sampling distribution.

00:54 Okay, actually, so in this case, the mean would not equal the one sample mean the mean would equal the mean of the sample means.

01:05 We would expect that also to be the mean of the population.

01:08 We have that the shape would approximate the shape of the population.

01:11 That is false.

01:13 Again, like i said, the sample size is sufficiently large that the sample means would be distributed normally regardless of the original underlying distribution.

01:22 Then, compared to the population variability, the variability would be reduced by a factor equal to the square root of 35.

01:29 That is true.

01:32 We have that the standard deviation of the sample means is going to be equal to the standard deviation of the population divided by the square root of the sample size...

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