Question

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 equal to the population standard deviation.

i) If the sample size increases, but p stays the same, then the standard deviation of the sampling distribution of the sample proportion decreases.

j) Extreme values should always be excluded from subsequent analysis.

Answer #1

f) **TRUE**

**REASON:** A weighted mean is preferred over an
unweighted mean because the final average number reflects the
relative importance of each observation and is thus more
descriptive than a simple average.

g) **FALSE**

**REASON:** A z-score is not a percentile because a
z-score describes the position of a raw score in terms of its
distance from the mean, when measured in standard deviation
units.

h) **TRUE**

**REASON:** The sample variance is more often less
than the population variance due to the skewed nature of the
distribution of the unbiased sample estimate.

i)**TRUE**

**REASON:** Because with bigger sample sizes, the
sample mean becomes more accurate estimate of the parametric mean,
so the standard deviation of the sampling distribution of the
sample proportion decreases.

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 3 sentences.
i) A p-value is the probability that the null hypothesis is
false. ii) A chi-square test statistic can never be negative.
iii) If we reject the null hypothesis that a population
proportion is equal to a specific value, then that specific value
will not be contained in the associated confidence interval.
iv) If...

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.

State whether each of the following is True or
False.
a. A smaller sample could provide less sampling error than a larger
sample from a given population.
b. The correct critical value a lower tail hypothesis test when
sigma is unknown, the sample size = 15, and alpha = 0.05 is
-1.645.
c. A larger sample size can reduce the potential for extreme
sampling error.
d. It is impossible for the population mean to equal the mean of a
sample...

Assignment Directions
Answer the following critical thinking questions in this forum.
Feel free to copy the questions and paste into your reply so that
you cover each one. Use complete sentences and proper statistical
terminology in all posts.
Read the instructors response to the questions.
Read the answers of some of your peers.
Make a reply to your own post with any corrections to your
responses.
Questions:
What are the requirements on sampling and the population so
that the distribution...

1. Are the following statements TRUE
or FALSE?:
(a) According to the Central Limit Theorem, given a large sample
size (N > 30), then a normal probability plot of the
same data would necessarily follow a straight line.
(b) A 95% confidence interval for a population mean that does
not include zero would also mean that a hypothesis test on the same
data would yield a significant result at the .05 level.
(c) The mean of a t-distribution with 5...

Which of the following statements is not consistent with
the Central Limit Theorem?
1. The Central Limit Theorem applies to non-normal population
distributions.
2. The standard deviation of the sampling distribution will be
equal to the population standard deviation.
3. The sampling distribution will be approximately normal when
the sample size is sufficiently large.
4. The mean of the sampling distribution will be equal to the
population mean.

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...

True or False: a.) Variance is the mean of the squared deviation
score. b.) For any population, a z-score of +1.00 corresponds to a
location above the mean by one standard deviation. c.) In a
distribution with s=8, a score of X=64 corresponds to z=-.50. The
mean for this sample will be M=60. d.) Transforming X values into
z-scores will not change the shape of the distribution. e.) One
advantage of transforming X values into z-scores is that the
transformation...

Identify each of the following statements as either TRUE or
FALSE.
a) FalseTrueClick for
List In a hypergeometric distribution, the trials
are independent of each other.
b) TrueFalseClick for
List In a hypergeometric distribution, if x is the
number of successes in a sample size of n, then n - x is the number
of failures in the sample.
c) FalseTrueClick for
List If X is a hypergeometric random variable,
then X can take on n different values.
d) TrueFalseClick for
List In a...

1) Determine whether the statements are true/ false.
a. T F
The probability of making a type II error is related to
the power of a statistical test
b. T
F When I compare
two estimates of the mean, the one with a smaller standard error
has
less precision
c. T F
If I do
cluster sampling, the sample mean is always within the 95%
confidence interval.
d. T
F
If I do simple random sampling, the true...

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