Question

1) Which of the following statements is correct about the standard normal distribution and t distribution?

a) standard normal distribution is used to eliminate population mean, while t distribution is used to estimate population standard deviation

b) t distribution is always centered at 0, while the center of a standard normal destruction depends on the sample mean

c) none of the 3 answer choices

d) standard normal distribution curve is higher than t distribution curve at the tails

2) If we know the population standard deviation and use sample mean to estimate the population mean, which of the following statements is correct?

a) it is not affected by our sample mean

b) it is smaller if we use a higher level of confidence

c) it may be larger or smaller than the size of confidence interval, depending on the confidence level

d) it is larger if our sample size is bigger

Answer #1

1)C is correct option.

None of the 3 answer choices are correct.

The normal distribution is used when the population distribution
of data is assumed normal. It is characterized by the mean and the
standard deviation of the data. A sample of the population is used
to estimate the mean and standard deviation.

The t statistic is an estimate of the standard error of the mean of
the population or how well known is the mean based on the sample
size.

t distribution is higher at tails.

In 2 please mention what is the meaning of 'it' in the options.Otherwise the correct option cannot be chosen.

Which of the following statements about the sampling
distribution of the sample mean, ¯xx¯ , is the correct?
1The distribution is normal regardless of the shape of the
population distribution, as long as the sample size, n, is large
enough.
2The distribution is normal regardless of the sample size, as
long as the population distribution is normal.
3The distribution's mean is the same as the population mean.
4The distribution's standard deviation is smaller than the
population standard deviation.
5All of...

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...

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.

Which of the following about a normal distribution is true?
The sample mean equals the population mean if the sample and the
population are both normally distributed
The area under the curve to the right of mean is .50
It is a classical probability distribution where each outcome is
equally likely.
The smaller the standard deviation, the flatter the curve will
be

Answer the following about T-Test & T-distributions:
1. Which of the following statements related to the
t-distribution is not true?
Select one:
a. Since the population standard deviation is usually unknown,
the standard error of the sample mean is estimated using the sample
standard deviation as an estimator for the population standard
deviation. The formula is s/sqrt(n).
b. The population must be t-distributed in order to use the
t-distribution.
c. Like the Normal distribution, the t-distribution is symmetric
and unimodal....

For the standard normal distribution, compute Z0.69.
Use Excel and round the answer to two decimal places.
Consider the following test performed with the level of
significance 0.01: A random sample of size 28 is obtained from a
normally distributed population. The population standard deviation
is equal to 3.6. The sample mean happened to be 24. For this
hypothesis test, what will be the critical value (the relevant
z-alpha)? Round the answer to three decimal
places.
A probability distribution of all...

1. To estimate the mean of a population with unknown
distribution shape and unknown standard deviation, we take a random
sample of size 64. The sample mean is 22.3 and the sample standard
deviation is 8.8. If we wish to compute a 92% confidence interval
for the population mean, what will be the t multiplier? (Hint: Use
either a Probability Distribution Graph or the Calculator from
Minitab.)

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...

Use the standard normal distribution or the t-distribution to
construct a 99% confidence interval for the population mean.
Justify your decision. If neither distribution can be used,
explain why. Interpret the results. In a random sample of 13
mortgage institutions, the mean interest rate was 3.59% and the
standard deviation was 0.42%. Assume the interest rates are
normally distributed.
Select the correct choice below and, if necessary, fill in any
answer boxes to complete your choice.
A. The 99% confidence...

0. Consider a distribution of raw scores in which the
distribution is normal. Consider that each and every score is
converted into a standard score (a z score), such that the
resulting distribution is a normal distribution of standard scores
(a standard normal distribution, also known as the SND). The
standard normal distribution has all the following characteristics,
except
a. The distribution is bell-shaped.
b. The distribution is symmetrical.
c. The mean, median, and mode of the distribution are equal...

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