Question

Which of the following statement about the sampling distribution of proportion is true?

Select one:

a. Its mean equals to the population proportion.

b. Its standard error equals to the population standard deviation.

c. It is approximately normally distributed if n ≥ 30.

d. It is approximately normally distributed if the population is normally distributed.

Answer #1

Solution:

Correct option is

**a. Its mean equals to the population
proportion.**

Explanation:

We have to discuss the sampling distribution of proportion , not mean.

Let p be the population proportion.

n be the sample size.

Let be the sample proportion.

The sampling distribution of is approximately normal with

mean = = p

SD = =

The necessary condition for the distribution is to be normal is that ,

n * p and n* (1 - p) both are 10

Correct option is

a. Its mean equals to the population proportion.

Which of the following is true?
The shape of the sampling distribution of sample proportion is
always bell-shaped.
As n increases, the mean of the sampling distribution of sample
proportion gets closer to the population proportion.
The shape of the sampling distribution of sample proportion
becomes approximately normal as n gets large.
The shape of the sampling distribution of sample proportion gets
closer to the shape of the population distribution as n gets
large.

Which of the following is false?
The sampling distribution of the sample proportion is the
distribution of values of the sample proportion from all possible
samples of size n drawn from a population.
When a sample proportion is calculated, the population from
which the sample comes is discrete.
The variance of the sample proportion is equal to the variance
of a binomial random variable divided by the sample size
squared.
The sampling distribution of the sample proportion is
approximately normally...

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.

Question 2: Which of the following statements about the
sampling distribution of means is not true?
A. A sample distribution's mean will always equal the parent
population distribution's mean
B. The sampling distribution of means approximates the normal
curve.
C. The mean of a sampling distribution of means is equal to the
population mean.
D. The standard deviation of a sampling distribution of means is
smaller than the standard deviation of the population.

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

Which of the following is true regarding the sampling
distribution of the mean for a large sample size?
Select one:
a. It has the same shape, mean, and standard deviation as the
population.
b. It has the same shape and mean as the population, but has a
smaller standard deviation.
c. It has a normal distribution with the same mean as the
population but with a smaller standard deviation.
d. It has a normal distribution with the same mean and...

Which of the following statements are TRUE?
Note that there may be more than one correct answer; select all
that are true.
1. a) All else being equal, the standard deviation of the
sampling distribution of the sample mean will be smaller for n = 10
than for n = 40.
b) The value of a statistic does not vary from sample to
sample.
c) Statistics have sampling distributions.
d) The value of a parameter does not vary from sample...

Which of the following is NOT true regarding the sampling
distribution of the mean (Sample mean X-bar) for a large sample
size (sample size is greater than 36)? A. It has the same mean as
the population. B. It has a smaller standard deviation than the
population standard deviation. C. Approximately it follows a normal
distribution. D. It has the same distribution as the
population.

Which of the following statements are true?
I. The sampling distribution of ¯xx¯ has standard deviation σ√nσn
even if the population is not normally distributed.
II. The sampling distribution of ¯xx¯ is normal if the population
has a normal distribution.
III. When nn is large, the sampling distribution of ¯xx¯ is
approximately normal even if the the population is not normally
distributed.
I and II
I and III
II and III
I, II, and III
None of the above gives...

Which of the following statements are true?
I. The sampling distribution of ¯xx¯ has standard deviation σ√nσn
even if the population is not normally distributed.
II. The sampling distribution of ¯xx¯ is normal if the population
has a normal distribution.
III. When nn is large, the sampling distribution of ¯xx¯ is
approximately normal even if the the population is not normally
distributed.
I and II
I and III
II and III
I, II, and III
None of the above gives...

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