Question

1.      There is a population of three people: Xerxes, Yasmin, and Zoe. [Note: this is a...

1.      There is a population of three people: Xerxes, Yasmin, and Zoe. [Note: this is a population, not a sample.] They are asked how many books they read last month. Xerxes read 2 books, Yasmin read 4 books, and Zoe read 12 books. We are too lazy to poll the entire population, so we take a sample of two (with replacement and order matters). Please draw the sampling distribution of the mean of a sample of size two.

2.      Continuing with the above example, what is the probability that the sample average will be within two books of the population average?

3.      Continuing with the above example, what is the standard error of the sampling distribution of the mean for a sample of size two? (In other words, what is the standard error for the distribution drawn in the first question.)

4.      Continuing with the above example, calculate the standard error of the sampling distribution of the mean for a sample of size two in a completely different way than you calculated it in question 3.

Homework Answers

Answer #1

1)

Th e books reads by three people: Xerxes(X), Yasmin(Y), and Zoe(Z)

Population Books read
X 2
Y 4
Z 12

Now, the ordered sampling with replacement of size two are,

Sample Average Books read
XY (2+4)/2=3
XZ (2+12)/2=7
YZ (4+12)/2=8

The mean and standard deviation of samples,

2)

Probability that the sample average will be within two books of the population average is,

The probability is obtained by converting to standard normal distribution,

3)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
There is a population of four people: Amy, Ben, Clara, and Donna. [Note: this is a...
There is a population of four people: Amy, Ben, Clara, and Donna. [Note: this is a population, not a sample.] They are asked how many apples they ate last month. Amy ate 3 apples, Ben ate 5 apples, Clara ate 11 apples, and Donna ate 1 apple. We are too lazy to poll the entire population, so we take a sample of two (with replacement and order matters). We then calculate the mean of the sample in order to estimate...
There is a population of four people: Amy, Ben, Clara, and Donna. [Note: this is a...
There is a population of four people: Amy, Ben, Clara, and Donna. [Note: this is a population, not a sample.] They are asked how many apples they ate last month. Amy ate 3 apples, Ben ate 5 apples, Clara ate 11 apples, and Donna ate 1 apple. We are too lazy to poll the entire population, so we take a sample of two (with replacement and order matters). What is the probability of the sample mean equaling the population mean?
2-4 There is a population of four people: Amy, Ben, Clara, and Donna. [Note: this is...
2-4 There is a population of four people: Amy, Ben, Clara, and Donna. [Note: this is a population, not a sample.] They are asked how many apples they ate last month. Amy ate 3 apples, Ben ate 5 apples, Clara ate 11 apples, and Donna ate 1 apple. We are too lazy to poll the entire population, so we take a sample of two (with replacement and order matters). What is the probability of the sample mean equaling the population...
1. How many sample of size 4 can be drawn without replacement from the population 0,3,6,3,18?compute...
1. How many sample of size 4 can be drawn without replacement from the population 0,3,6,3,18?compute the sampling distribution of the mean, then identify the relationship between the population and sampling distribution standard deviations?
Assume for a moment that we have a population distribution that is negatively skewed. Which probability...
Assume for a moment that we have a population distribution that is negatively skewed. Which probability distribution becomes normal as the size of the sample increases? population distribution sample distribution sampling distribution None of the above The standard error of the mean refers to the standard deviation of the... normal distribution population sample sampling distribution None of the above Which type of error can be quantitatively measured: sampling error non-sampling error both neither The purpose of statistical inference is to...
Suppose a population mean of 7 for some characteristic of interest and a standard deviation of...
Suppose a population mean of 7 for some characteristic of interest and a standard deviation of 9.6. A sample is drawn from this population of size 64. What is the standard error of the mean? What are the values of ?"̅ and ?"̅ for the sampling distribution of the mean then? Draw the curve that corresponds.
QUESTION 1 A standard error is the variance of the population distribution. the variance of the...
QUESTION 1 A standard error is the variance of the population distribution. the variance of the sampling distribution. the standard deviation of the sampling distribution the standard deviation of the population distribution. QUESTION 2 A confidence interval is constructed to bracket the sample mean. to bracket the margin of error. to bracket the population parameter. to bracket the sample statistic. QUESTION 3 A sampling distribution is the standard deviation of the estimated slope coefficient. the distribution of a statistic. the...
5. A random sample of 120 people is drawn from a population and asked how much...
5. A random sample of 120 people is drawn from a population and asked how much time each week they spend watching television. The population has a mean of 187 minutes with a standard deviation of 32 minutes. (a) Find the mean and standard error of the sampling distribution of ¯x. (b) What is the probability that this sample will have a mean that is at least 192 minutes? (c) What proportion of all samples of size 120 will have...
Consider a population of 5 weights identical in appearance but weighing 1, 3, 5, 7, and...
Consider a population of 5 weights identical in appearance but weighing 1, 3, 5, 7, and 9 ounces. a. Determine the mean and the variance of the population. b. Sampling without replacement from the above population with a sample size of 2, how many samples can you create? List them all. c. For each sample, compute the sample mean. d. Determine the mean of the population and the variance of . e. Compute the standard error of the mean.
Suppose we repeatedly take samples of size 100 from the population distribution, calculate a sample mean...
Suppose we repeatedly take samples of size 100 from the population distribution, calculate a sample mean each time, and plot those sample means in a histogram. The histogram we created would be an example of a (variable, population, distribution, sampling distribution???) . According to the central limit theorem, the histogram would have a shape that is approximately (left skewed, right skewed or normal???) , with mean  (give a number???) and standard deviation  (give a number??). The standard deviation of the statistic under...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT