Question

a. What is the difference between population mean and sample mean?

b. Describe the difference between point estimate and a confidence interval?

c. Describe the role that confidence level play in the confidence interval?

Answer #1

. Describe the difference between a "population" and a "sample."
What is a "representative sample"? What is the best way to achieve
representativeness in a sample?

What could be the explanation for the difference between the
sample mean and the population mean ?

A statistics practitioner took a random sample of 80
observations from a population with a standard deviation of 25 and
compute the sample mean to be 100.
(a) Estimate the population mean confidence interval with 90%
confidence level, 95% confidence level and 99% confidence
level.
(b) Describe the effect of increasing the confidence level on
the confidence interval.
(c) At 99% confidence level, if the population standard
deviation is reduced to 16, will the confidence interval be wider
or narrower?

A random sample of 24 observations is used to estimate the
population mean. The sample mean and the sample standard deviation
are calculated as 104.6 and 28.8,
respectively. Assume that the population is normally
distributed. Construct the 90% confidence interval for the
population mean. Then, construct the 95% confidence
interval for the population mean. Finally, use your answers to
discuss the impact of the confidence level on the width of the
interval.

A random sample of 14 observations is used to estimate the
population mean. The sample mean and the sample standard deviation
are calculated as 158.4 and 30.10, respectively. Assume that the
population is normally distributed. [You may find it useful
to reference the t table.]
a. Construct the 90% confidence interval for the
population mean. (Round intermediate calculations to at
least 4 decimal places. Round "t" value to 3 decimal
places and final answers to 2 decimal places.)
b. Construct...

1. The difference between a sample mean and the population mean
or the difference between the means of two random samples is
called: A. nonresponse error. B. selection bias. C. sampling error.
D. nonsampling error.
2. The manager of the customer service division of a major
consumer electronics company is interested in determining whether
the customers who have purchased a videocassette recorder over the
past 12 months are satisfied with their products. If there are 4
different brands of videocassette...

A random sample of 20 observations is used to estimate the
population mean. The sample mean and the sample standard deviation
are calculated as 152 and 74, respectively. Assume that the
population is normally distributed.
What is the margin of error for a 95% confidence interval for
the population mean?
Construct the 95% confidence interval for the population
mean.
Construct the 90% confidence interval for the population
mean.
Construct the 78% confidence interval for the population mean.
Hint: Use Excel...

A random sample is drawn from a population having σ = 15.
a. If the sample size is n = 30 and the sample mean x = 100,
what is the 95% confidence interval estimate of the population mean
µ?
b. If the sample size is n = 120 and the sample mean x = 100,
what is the 95% confidence interval estimate of the population mean
µ?
c. If the sample size is n = 480 and the sample...

Describe a confidence interval for the difference in means
between two population by stating
1. a pair of populations composed of the same type of individuals
and a quantitative variable on those populations,
2. sizes and degrees of freedom of samples from those
populations,
3. the means of those samples, and
4. the standard deviations of those samples. Then state
5. a confidence level and find
6. find the interval. Finally, perform a test of significance
concerning the difference in...

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.

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