Question

(a) If we have a distribution of *x* values that is more
or less mound-shaped and somewhat symmetric, what is the sample
size *n* needed to claim that the distribution of sample
means *x* from random samples of that size is approximately
normal?

*n* ≥

(b) If the original distribution of *x* values is known to
be normal, do we need to make any restriction about sample size in
order to claim that the distribution of sample means *x*
taken from random samples of a given size is normal?

YesNo

Answer #1

TOPIC:Normality assumption of the distribution of the sample mean.

A random sample of 36 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 14 and the sample
standard deviation is 2. Use a level of significance of 0.05 to
conduct a two-tailed test of the claim that the population mean is
13.5.
(a) Is it appropriate to use a Student's t
distribution? Explain.
Yes, because the x distribution is mound-shaped and
symmetric and σ is unknown.No, the x distribution
is skewed left. No, the x
distribution...

A random sample of 16 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 11 and the sample
standard deviation is 2. Use a level of significance of 0.05 to
conduct a two-tailed test of the claim that the population mean is
10.5.
(a) Is it appropriate to use a Student's t
distribution? Explain.
Yes, because the x distribution is mound-shaped and
symmetric and σ is unknown.No, the x distribution
is skewed left. No, the x
distribution...

A random sample of 36 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 9 and the sample
standard deviation is 2. Use a level of significance of 0.05 to
conduct a two-tailed test of the claim that the population mean is
8.5.
(a) Is it appropriate to use a Student's t
distribution? Explain.
Yes, because the x distribution is mound-shaped and
symmetric and σ is unknown.No, the x distribution
is skewed left. No, the x
distribution...

A random sample of 16 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 13 and the sample
standard deviation is 2. Use a level of significance of 0.05 to
conduct a two-tailed test of the claim that the population mean is
12.5.
(a) Is it appropriate to use a Student's t
distribution? Explain.
Yes, because the x distribution is mound-shaped and
symmetric and σ is unknown.No, the x distribution
is skewed left. No, the x
distribution...

A random sample of 25 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 11 and the sample
standard deviation is 2. Use a level of significance of 0.05 to
conduct a two-tailed test of the claim that the population mean is
10.5.
(a) Is it appropriate to use a Student's t distribution?
Explain.
Yes, because the x distribution is mound-shaped and symmetric
and σ is unknown.
No, the x distribution is skewed left.
No, the...

A random sample of 36 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 11 and the sample
standard deviation is 2. Use a level of significance of 0.05 to
conduct a two-tailed test of the claim that the population mean is
10.5.
(a) Is it appropriate to use a Student's t
distribution? Explain.
Yes, because the x distribution is mound-shaped and
symmetric and σ is unknown.No, the x distribution is
skewed left. No, the x
distribution...

A random sample of 25 values is drawn from a mound-shaped and
symmetrical
distribution. The sample mean is 10 and the sample standard
deviation is 2.
Use a level of significance of 0.05 to conduct a two-tailed test of
the claim that the
population mean is 9.5.
(a) Is it appropriate to use a Student’s t distribution?
Explain. How many degrees of freedom do we use?
(b) What are the hypotheses?
(c) Calculate the sample test statistic t.
(d) Estimate...

Suppose x has a mound-shaped distribution. A random sample of
size 16 has sample mean 10 and sample standard deviation 2.
(b) Find a 90% confidence interval for μ
(c) Interpretation Explain the meaning of the confidence
interval you computed.

Suppose x has a distribution with μ = 24 and
σ = 11.
1. If random samples of size n = 16 are selected, can
we say anything about the x distribution of sample
means?
2. If the original x distribution is normal, can
we say anything about the x distribution of random samples
of size 16?
3. Find P(20 ≤ x ≤ 25). (Round your answer to
four decimal places.)
___________________

Suppose x has a distribution with μ = 75 and
σ = 8.
(a) If random samples of size n = 16 are selected, can
we say anything about the x distribution of sample
means?
No, the sample size is too small.Yes, the x
distribution is normal with mean μx =
75 and σx =
0.5. Yes, the x distribution is
normal with mean μx = 75 and
σx = 2.Yes, the x
distribution is normal with mean μx =
75...

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