Question

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.

Answer #2

Solution:

Given sentence is

**TRUE**

Explanation :

Let X be a r.v.

If we take repeated samples form this population , then we obtain various values of sample means.This is sampling distribution of .

If X follows normal distribution , then the sampling distribution of is approximately normal(whatever the sample size)

If distribution of X is not normal, and sample size n > 30 then also the sampling distribution of is approximately normal.

So , answer is

True

answered by: anonymous

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.

True or False?
The sampling distribution of the sample mean of a non-normally
distributed population will also be normally distributed as long as
the sample size is greater than 10.
The sampling distribution of the sample mean of a normally
distributed population will not be normally distributed if sample
size is less than 30.

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.

6.63 True or False. The sample mean, x, will always be equal to
mx.
6.64 True or False. The sampling distribution of x is normally
distributed, regardless of the size of the sample n.
6.65 True or False. The standard error of x will always be
smaller than s.

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...

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.

In each case, determine if the distribution of the sample mean
(x-bar) is NORMALLY DISTRIBUTED, AT LEAST APPROXIMATELY NORMALLY
DISTRIBUTED, or CANNOT BE DETERMINED.
The population is known to be normally distributed, the sample
size is n = 56. a) can not be determined b) at least approximately
distributed c)normally distributed.
The population distribution is not known, sample size is n =
100. a) can not be determined b) at least approximately distributed
c)normally distributed.
The population is known to...

For each of the following statements, identify whether the
statement is true or false, and explain why. Please limit each
response to no more than 2 sentences.
f) A weighted mean is preferred over an unweighted mean (i.e. a
regular sample mean) when each observation has its own unique
weight.
g) A z-score is a percentile.
h) Assuming the population is normally distributed, the standard
deviation of the sampling distribution of the sample mean will
always be less than or...

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...

Indicate whether the following statement is true or false.
In hypothesis testing, the p-value should always be larger than
the selected level of significance.
True
False

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