1) Fully define and discuss the properties of the sampling distribution of the mean (1 pt)....

1) Fully define and discuss the properties of the sampling distribution of the mean (1 pt).

2) What does the central limit theorem tell us? Why does it work (an intuitive example was discussed in class) (2pt).

3) What are the conditions/assumptions necessary to run a Z-test? (1 pt.)

4) Consider randomly sampling from a theoretical normal distribution. (1 pt. each).

a. What is the probability that a single randomly sampled observation have a value above the mean?

b. What is the probability that observations from a random sample size of n=2 will both have values above the mean?

c. What is the probability that observations from a random sample size of n=4 will all have values above the mean?

d. What is the probability that observations from a sample size of n=8 will all have values above the mean?

Expert Solution

milcah answered 2 weeks ago

Define the sampling distribution of the mean

discuss what the mean of a sampling distribution is and describe how to calculate it using...

discuss what the mean of a sampling distribution is and describe how to calculate it using a specific example. Describe a scenario and explain finding the mean of a sampling distribution.

Define sampling distribution. b. Explain why the spread (variance) of a sampling distribution for estimating a...

Define sampling distribution. b. Explain why the spread (variance) of a sampling distribution for estimating a mean would be smaller than the spread (variance) of the whole population. c. Discuss what happens to the shape AND spread of a sampling distribution as sample size (n) is increased. d.Explain why it is essential that the sampling distribution be normally distributed (or t-distributed) in order to do the statistical inference procedures we use in Chapters 9, 10 and 11.

Explain how a sampling distribution is created. What does the mean (center) of the sampling distribution...

Explain how a sampling distribution is created. What does the mean (center) of the sampling distribution tell us? What is the standard deviation of the sampling distribution called and what does it tell us? Explain the central limit theorem. Why is it important for a sampling distribution of sample means and sample proportions to be normal? What requirement ensures that a sampling distribution for sample means is normal? What requirement ensures that a sampling distribution for sample proportion is normal?...

Discuss a sampling distribution by describing 1. A population, 2. A variable on the individuals in...

Discuss a sampling distribution by describing 1. A population, 2. A variable on the individuals in that population, 3. A standard deviation for that variable, and 4. The size of a sample from that population. Compare the 5. Center, 6. Variability, and 7. Shape of the sampling distribution of the mean of that sample with those of the population distribution. What does the sampling distribution tell us about the population?

,,1-The sampling distribution of the mean is...............? 2- The expected value of a random variable corresponds...

,,1-The sampling distribution of the mean is...............? 2- The expected value of a random variable corresponds to the notion of the ________ of a sample.? 3- A negative correlation coefficient indicates a linear relationship between variables where one variable increases as the other increases. Is T or F? 4- If a variable is removed from the regression model when the t-statistic is lesser than 1, ________.? 5- If we sample with replacement from a finite population, the sampling distribution of the...

1. The sampling distribution of the sample mean is approximately normal for all sample sizes. a....

1. The sampling distribution of the sample mean is approximately normal for all sample sizes. a. true b. false 2. If all possible samples of the same size have the same chance of being selected, these samples are said to be random samples. a. true b. false 3. The population of sample means of every possible sample size (n) is known as the ______ distribution of the mean. 4. A sample size of 49 drawn from a population with a...

The purpose of this is to demonstrate the sampling distribution of the sample mean when the...

The purpose of this is to demonstrate the sampling distribution of the sample mean when the data is generated from an exponential distribution (at rate 2.0) as sample size increases. Describe and compare the sampling distributions of the sample mean for sample sizes n=5, n=20, n=40. Do this by simulating samples at least 5000 times. R-code for generating a sample of size n=10 from exponential distribution at rate 2.0 is >rexp(n=10, rate=2.0)

What is the sampling distribution of the sample mean? Provide examples.

a) How does the mean of any sampling mean distribution compare to the population mean? b)...

a) How does the mean of any sampling mean distribution compare to the population mean? b) Explain what happens to the spread of the sample mean distribution as the sample size increases based on the results observed in this lab.

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