Question

Assuming a random variable X with the following distribution

X= last digit of your student number and second last digit number of your student number

If the last two digits of your student number are the same, use 1 and 0 for the question.

The Probability X is the last digit of your student number is 0.6

The Probability X is the last digit of your student number is 0.4

- What is the population mean and variance of X?
- Show the sampling distribution the Xbar when the sample size is 5.
- What is the mean and variance of X bar ?
- When the sample size is larger than 25, how do you think Xbar is distributed? What is the mean and variance of Xbar?

Answer #1

For the population of one town, the number of siblings is a random
variable whose relative frequency histogram has a reverse J-shape.
Let x-bar denote the mean number of siblings for a random sample of
size 30. For samples of size 30, which of the following statements
concerning the sampling distribution of the mean is true?
x-bar is normally
distributed.
The distribution of
x-bar has a reverse J-shape.
x-bar is approximately
normally distributed.
None of the above
statements is true.

5. Let x be a random variable with the following
probability distribution.
x P(x)
1 0.6
5 0.4
Consider a sample of size 3 from the population, and let
x be the sample mean. Construct a probability distribution for
x.
Not sure how this was answered
correct Answer
x P(x)
1 .216
7/3 .432
11/3 .288
5 .064

Indicate whether the
following statement is true or false.
The sampling
distribution of the sample mean (x-bar) will at least approximately
be normally distributed either if X is normally distributed or if
the sample size (n) is larger than 30.

a. What is the standard error of a sampling
distribution? (out of the following)
the mean, the probability, the bias, the standard deviation, or
the variance
b. What is the standard deviation of a sampling
distribution called? (out of the following)
the spread, the variance, the standard error, the mean, the
standard variance
c. List two unbiased estimators and their
corresponding parameters. (Select all that apply out of the
following.)
μ is an unbiased estimator for x-bar, p is an...

Let the random variable X follow a Normal distribution with
variance σ2 = 625.
A random sample of n = 50 is obtained with a sample mean, X-Bar
of 180.
What is the probability that μ is between 198 and 211?
What is Z-Score1 for μ greater than 198?

In the following probability distribution, the random variable
x represents the number of activities a parent of a
6th to 8th-grade student is involved in. Complete parts (a)
through (f) below.
x
0
1
2
3
4
P(x)
0.395
0.075
0.199
0.195
0.136
(a) Verify that this is a discrete probability
distribution.
This is a discrete probability distribution because the sum of
the probabilities is ___and each probability is ___ (Less than or
equal to 1; Greater than or equal...

A random variable X is normally distributed. It has a mean of
254 and a standard deviation of 21.
List the givens with correct symbols:
? (σ N X̄ μ s X p n) = 254
? (X̄ n σ s X p μ N) = 21
a) If you take a sample of size 21, can you say what the shape of
the sampling distribution for the sample mean is?
? Yes No
Why or why not? Check all...

6. Let d= X -Y, where X and Y are
random variables with normal distribution, and X and Y are
independent random variables. Assume that you know both the mean
and variance of X and Y, if you have random samples
from X and Y with equal sample size, what is the sampling
distribution for the sample means of d(assuming X and Y are
independent)?

True or false:
1. When constructing a confidence interval for a sample
Mean, the t distribution is appropriate whenever the sample size is
small.
2. The sampling distribution of X (X-bar) is not always
a normal distribution.
3. The reason sample variance has a divisor of n-1
rather than n is that it makes the sample standard deviation an
unbiased estimate of the population standard
deviation.
4. The error term is the difference between the actual
value of the dependent...

TRUE OR FALSE:
1. The sampling distribution of (X-bar) is
always a normal distribution according to the Central limit
theorem.
4. If the sampled population is a normal distribution, then the
sampling distribution of (X-bar is normal only for a
large enough sample size.
5. If p=.8 and n=50, then we can conclude that the sampling
distribution of the proportions is approximately a normal
distribution.
8. Assuming the same level of significancea, as the
sample size increases, the critical t-value...

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