Question

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.

d. The t-distribution is generally bell-shaped, and the shape of the t-distribution gets closer to the shape of the Normal distribution as sample size increases.

**As sample size increases, and all summary statistics
remain the same, what will happen to the test statistics for the
z-test and the t-test?**

**Select one:**

a. They will both increase in magnitude

b. They will not change

c. The t-statistic will increase in magnitude, the z-statistic will not

d. They will both decrease in magnitude

e. The z-statistic will increase in magnitude, the t-statistic will not

f. None of these are true.

Note: I know for question #2 that it is not f. and for #1 I think that the answer is b?

Answer #1

1)

we use t distribution when given data is normally distributed and sample size is small or population standard deviation is unknown and we use sample s.d as the best estimate

As we use t distribution when data is normally distributed so, it is symmetrical like normal distribution

And yes as the sample size increases it approaches the standard normal distribution

So, only false statement is

b. The population must be t-distributed in order to use the t-distribution

2)

Test statistics z or t = (sample mean - claimed.mean)/(s.d/√n)

Or ((sample mean - claimed mean)*√n)/(s.d)

So, test statistics is directly proportional to the sample size n

So, answer is

a. They will both increase in magnitude

Which of the following is true about the one sample z-test and
one sample t-test:
for a t-test, the population mean and standard deviation are
needed.
The z and t-tests are identical in terms of the amount of
information needed.
for a t-test only the sample mean is needed.
for a z-test the population mean and standard deviation are
needed.
The z and t-tests are identical except for the size of the
sample used.

Which of the following statements are TRUE
Note that there may be more than one correct answer; select all
that are true.
a)
The power of a test is only influenced by the hypothesized
parameter value, and not the true parameter value.
b)
For a two-sided alternative hypothesis, as the difference
between the true parameter value and the hypothesized parameter
value increases, the probability of a Type I error increases.
c)
It is desirable to have tests with high power,...

Which of the following statements is not true for sampling
distributions?
a. A sampling distribution is necessary for making confidence
statements about an unknown population parameter.
b. A sampling distribution depends on the nature of the
population being sampled.
c. When sampling at random from a normal population, the
sampling distribution for the sample average is a normal
distribution.
d. None of the above.
AND
TRUE or FALSE
Assume a random sample of size n is from a normal population....

1. Which of the following is a major difference between a
hypothesis test with a t statistic and the test with a z-score?
a.
You must know the population standard deviation for the z-score
but not for the t statistic.
b.
You use the normal distribution table to find critical values
for t but not for z.
c.
You must know the population median for the z-score but not for
the t statistic.
d.
There are no major differences between...

Which of the following is true about Student’s t-models?
Group of answer choices
A. They are unimodal and symmetric.
B. They have fatter tails than the Normal model.
C. As the degrees of freedom increase, the t-models look more
and more like the Normal Model
D. All of the above.

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...

Find the F-test statistic to test the claim that the population
variances are equal. Both distributions are normal. The standard
deviation of the first sample is 3.3895
3.7904 is the standard deviation of the second sample.

Determine which distribution should be used in a
hypothesis test with the following information, or if it is not
appropriate to conduct a hypothesis test.
(a) The claim is μ
≤ 86. The sample data is: n = 29, ¯x
= 85.2, and s = 8. The population standard deviation is
unknown, and the population is not even approximately normally
distributed.
Normal (z) distribution (or
Z-Test on the calculator)
Student t distribution (or
T-Test on the calculator)
A...

Which of the following is NOT a step in hypothesis testing?
Select one: a. Find the confidence interval. b. Use the level of
significance and the critical value approach to determine the
critical value of the test statistic c. Formulate the null and
alternative hypotheses d. Use the rejection rule to solve for the
value of the sample mean corresponding to the critical value of the
test statistic. When population standard deviation (σ) is unknown,
we use sample standard deviation...

10. For a particular scenario, we wish to test the hypothesis
H0 : p = 0.52. For a sample of size
50, the sample proportion p̂ is 0.42. Compute the value of
the test statistic zobs. (Express your answer
as a decimal rounded to two decimal places.)
4. For a hypothesis test of
H0 : μ = 8
vs.
H0 : μ > 8,
the sample mean of the data is computed to be 8.24. The
population standard deviation is...

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