Question

a.

How well do the 95% confidence intervals do at capturing the true population mean when

samples sizes are small?

b. Does a larger sample size mean that the intervals are more likely to capture the true population value? Why? Note THIS is an

important concept and relates back to the Sampling Distribution of Sample Means.

Answer #1

a. How well do the 95% confidence intervals do at capturing the true population mean when sample sizes are small?

When the sample size is small, the width of confidence interval
increases due to a decrease in the sampling error and a large
amount of data is collected in the confidence interval. This means
that the 95% confidence intervals are **more likely**
of capturing the true population mean when sample sizes are
small.

b. Does a larger sample size mean that the intervals are more likely to capture the true population value? Why?

Please note that with the increase in sample size, the width of
the confidence interval decreases due to an increase in the
sampling error. This means that the 95% confidence intervals are
**less likely** of capturing the true population mean
when sample sizes are large.

1. Develop 90 %, 95 %, and 99% confidence intervals for
population mean (µ) when sample mean is 10 with the sample size of
100. Population standard deviation is known to be 5.
2. Suppose that sample size changes to 144 and 225. Develop
three confidence intervals again. What happens to the margin of
error when sample size increases?
3. A simple random sample of 400 individuals provides 100 yes
responses. Compute the 90%, 95%, and 99% confidence interval for...

a. Compute the 95% and 99% confidence intervals on the mean
based on a sample mean of 50 and population standard deviation of
10, for a sample of size 15.
b. What percent of the 95% confidence intervals would you expect
to contain µ? What percent of the 95% confidence intervals would
you expect to contain x̅? What percent of the 95% confidence
intervals would you expect to contain 50?
c. Do you think that the intervals containing µ will...

The sample mean always lies at the center of the
confidence interval for the true population mean ( µX
).
The sample mean is also known as the best point estimate
for µX .
The true population mean is always in a 90% confidence
interval for µX .
If one-hundred (100) 95% confidence intervals for µX are
created from some population, the true population mean is likely to
be in approximately 95 of these 100 confidence
intervals.

1.
The confidence intervals for the population proportion are
generally based on ________.
the t distribution when the population standard deviation is not
known
the z distribution
the t distribution
the z distribution when the sample size is very small
2.
The difference between the two sample means 1
– 2 is an interval estimator of the difference
between two population means μ 1 – μ 2.
True
False
3.
Excel does not have a special function that allows to
calculate t values.
True...

Question 1.
Which of the following is the CORRECT interpretation of a 95%
confidence interval?
a) There is a 95% probability that the interval contains the
population value
b) There is a 95% chance that the true population value is
inside the interval
c) if we sampled from a population repeatedly and created
confidence intervals, 95% of those confidence intervals would
contain the population mean
d) We are 95% sure of the sample statistic
Question 2.
What is the mean...

Assuming that the population is normally distributed, construct
a 95% confidence interval for the population mean for each of the
samples below. Explain why these two samples produce different
confidence intervals even though they have the same mean and
range.
Sample A: 1 4 4 4 5 5 5 8
Sample B: 1 2 3 4 5 6 7 8
a. Construct a 95% confidence interval for the population mean
for sample A.
b. Construct a 95% confidence interval for...

Assuming that the population is normally distributed, construct
a 95% confidence interval for the population mean for each of the
samples below. Explain why these two samples produce different
confidence intervals even though they have the same mean and
range.
Sample A: 1 3 3 4 5 6 6 8
Sample B: 1 2 3 4 5 6 7 8
Construct a 95% confidence interval for the population mean for
sample A.
Construct a 95% confidence interval for the population...

Which of the following statements is true?
The 95% confidence interval is wider than the 99% confidence
interval.
The ONLY way to reduce the width of a confidence interval is to
reduce the confidence level.
The required sample size for a population mean is ONLY
dependent on population variance.
Given population variance and sampling error, higher confidence
level results in larger sample size.

A random sample of n individuals were selected. A 95% confidence
interval ($52,000 to $70,000) was constructed using the sample
results.
Which of the following statement(s) is/are true? (Can choose
answer more than 1)
If all possible samples of size n were drawn from this
population, about 95% of the population means would fall in the
interval ($52,000 to $70,000).
We do not know for sure whether the population mean is in the
interval $52,000 and $70,000.
If all possible...

A random sample of n individuals were selected. A 95% confidence
interval ($52,000 to $70,000) was constructed using the sample
results.
Which of the following statement(s) is/are true? ( Can choose
more than one answer)
If all possible samples of size n were drawn from this
population, about 95% of the population means would fall in the
interval ($52,000 to $70,000).
We do not know for sure whether the population mean is in the
interval $52,000 and $70,000.
If all...

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