Question 1

In your own words, try to explain the meaning and importance of the central limit theorem.

Accepted Answer

This states that as sample sizes increase, the sampling distribution of the mean looks more and more like a normal distribution. With sample sizes of 30 or more the sampling distribution of the mean will be a normal distribution, which allows one to calculate probabilities based on the normal distribution.

Question 2

Suppose that instead of having a sample of 25 in question #7, I had a sample of 100. Tell me how this would affect the results and why it makes sense that the results would be affected in this way.

Accepted Answer

If my sample size were 100, my standard error would be smaller (because larger samples should look more like the population, therefore reducing error). With a smaller standard error in the denominator of the formula for calculating a z score, I would end up with a larger z score. Larger z scores would be associated with smaller probabilities, so the chances of getting a sample mean of 11 when the population mean is 10 would be much smaller than .1056, if the sample was randomly selected and the n = 100. Here's what it would look like:
 $\sigma_{\bar{x}}$ = 
 $\frac{4}{\sqrt{100}}$ 
 = 4/10= .4
Now, to calculate my z score I go: z = 
 $\frac{11-10}{.4}$ 
$\rightarrow$1/.4 = 2.5.
Area beyond z is 1 - .9938 = .0062.

Question 3

Suppose that in the population of American college students the average number of alcoholic drinks consumed per week is 12. What is the probability of randomly selecting a sample (n = 16) with a mean of 10 and a standard deviation of 4? (Hint: Tell me the two probabilities it will be between using a 2-tailed value)

Accepted Answer

So I do not know the population standard deviation here, which means I'll have to look in Appendix B using the t values. First, I must calculate a standard error of the mean:
 $S_{\bar{x}}$ = 4/square root of 16 $\rightarrow$ 4/4 $\rightarrow$ 1.
Next I calculate a t value: t = 10 - 12/1 = -2/1 = -2.00.
My degrees of freedom will be 16 = 1 = 15.
So in Appendix B, looking at 15 degrees of freedom I find a value of 1.753 and a value of 2.131. These are the two closest values to 2.00. Then I look up at the top of the table and find that these correspond with alpha levels of .10 and .05. So the best I can do is say that the probability of getting a sample mean of 10 from this population, when the sample is randomly selected and n = 16, is between 5% and 10%.

Question 4

Please tell me the definition of "standard error" and then tell me, in your own words, what the standard error of the mean tells you.

Accepted Answer

A standard error is the average differen

Question 5

Suppose that I am interested in creating a sampling distribution of the mean. The sample sizes are 40 and the population is undergraduate students. Given this information, tell me how you would create a sampling distribution of the mean for the variable of calories consumed per day.

Accepted Answer

Select one random sample of 40, calculat

Question 6

Take a look at the formulas for calculating the standard error of the mean in Chapter 6. Explain why it makes sense to have the standard deviation in the numerator and the sample size in the denominator. (When I say "makes sense" I mean both mathematically and conceptually. In other words, why does it make sense that as the standard deviation increases the standard error also increases? And why does it make sense that as the sample size increases the standard error decreases?)

Accepted Answer

Mathematically it makes sense because as

Question 7

Suppose that in the population of chickens, the average number of feathers per chicken is 1000 with a standard deviation of 200. Suppose that I select a random sample of 64 birds from this population. What is the probability that this sample will have a mean of 950 feathers or fewer?

Accepted Answer

Standard error: 
 @#LAT-DLM&

Question 8

When using standard errors to calculate probabilities of events occurring by chance, how do you know when to use z scores and when to use t values?

Accepted Answer

Use z scores when you know the populatio

Question 9

Why does it make sense that a larger sample size will produce a smaller standard error of the mean?

Accepted Answer

The larger the sample the smaller the st

Question 10

Suppose that I know that in the population of bees in California, the average number of flowers pollinated per day is 10 with a standard deviation of 4. I select a random sample of 25 California bees. What is the probability that my sample mean will be 11 or more flowers pollinated?

Accepted Answer

Because I already know the population st

In your own words, try to explain the meaning and importance of the central limit theorem.

Suppose that instead of having a sample of 25 in question #7, I had a sample of 100. Tell me how this would affect the results and why it makes sense that the results would be affected in this way.

Please tell me the definition of "standard error" and then tell me, in your own words, what the standard error of the mean tells you.

Suppose that I am interested in creating a sampling distribution of the mean. The sample sizes are 40 and the population is undergraduate students. Given this information, tell me how you would create a sampling distribution of the mean for the variable of calories consumed per day.

Suppose that in the population of chickens, the average number of feathers per chicken is 1000 with a standard deviation of 200. Suppose that I select a random sample of 64 birds from this population. What is the probability that this sample will have a mean of 950 feathers or fewer?

When using standard errors to calculate probabilities of events occurring by chance, how do you know when to use z scores and when to use t values?

Why does it make sense that a larger sample size will produce a smaller standard error of the mean?

Suppose that I know that in the population of bees in California, the average number of flowers pollinated per day is 10 with a standard deviation of 4. I select a random sample of 25 California bees. What is the probability that my sample mean will be 11 or more flowers pollinated?

Introduction to Social Science Research Principles and Terminology

Measures of Central Tendency

Measures of Variability

The Normal Distribution

Standardization and Z Scores

Statistical Significance, Effect Size, and Confidence Intervals

T Tests

One-Way Analysis of Variance

Factorial Analysis of Variance

Repeated-Measures Analysis of Variance

Correlation

Regression

Nonparametric Statistics

Factor Analysis and Reliability Analysis: Data Reduction Techniques

Person-Centered Analysis

Filters

Exam 6: Standard Errors

In your own words, try to explain the meaning and importance of the central limit theorem.

Suppose that instead of having a sample of 25 in question #7, I had a sample of 100. Tell me how this would affect the results and why it makes sense that the results would be affected in this way.

Please tell me the definition of "standard error" and then tell me, in your own words, what the standard error of the mean tells you.

Suppose that I am interested in creating a sampling distribution of the mean. The sample sizes are 40 and the population is undergraduate students. Given this information, tell me how you would create a sampling distribution of the mean for the variable of calories consumed per day.

Suppose that in the population of chickens, the average number of feathers per chicken is 1000 with a standard deviation of 200. Suppose that I select a random sample of 64 birds from this population. What is the probability that this sample will have a mean of 950 feathers or fewer?

When using standard errors to calculate probabilities of events occurring by chance, how do you know when to use z scores and when to use t values?

Why does it make sense that a larger sample size will produce a smaller standard error of the mean?

Suppose that I know that in the population of bees in California, the average number of flowers pollinated per day is 10 with a standard deviation of 4. I select a random sample of 25 California bees. What is the probability that my sample mean will be 11 or more flowers pollinated?

Introduction to Social Science Research Principles and Terminology

Measures of Central Tendency

Measures of Variability

The Normal Distribution

Standardization and Z Scores

Statistical Significance, Effect Size, and Confidence Intervals

T Tests

One-Way Analysis of Variance

Factorial Analysis of Variance

Repeated-Measures Analysis of Variance

Correlation

Regression

Nonparametric Statistics

Factor Analysis and Reliability Analysis: Data Reduction Techniques

Person-Centered Analysis

Filters