1.
Discuss
the importance of constructing confidence intervals for the population mean by
answering these questions.
- What are confidence intervals?
- What is a point estimate?
- What is the best point estimate for the population mean? Explain.
- Why do we need confidence intervals?
Answer and Explanation:
|
Confidence interval is a range of values that is
likely to contain the true population parameter.
A point estimate is an estimator that produces a
single value as opposed to a range of values produced by a confidence
interval. The best point estimate for the population mean is
(the sample mean)
because it is unbiased.
In research, it is often difficult or impossible
to obtain an exact population mean especially when the population under
study is large. In this case, a sample mean is used to estimate population
mean. In order to obtain an estimate while considering errors that might
occur, we come up with a range of values that is likely to contain the true
population mean.
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- Using the data from the Excel workbook, construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. Include a statement that correctly interprets the confidence interval in context of the scenario.
Hint: Use the sample mean and sample standard deviation from
Deliverable 1.
Answer and Explanation:
|
We calculate the confidence interval for the
mean using Excel and we obtain the following results.
If we take 100 samples of employees from the
same population, the mean salary of the employees would lie between
60332.35 and 64279.91in approximately 95 of the samples.
|
- Using the data from the Excel workbook, construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. Include a statement that correctly interprets the confidence interval in context of the scenario.
Hint: Use the sample mean and sample standard deviation from
Deliverable 1.
Answer and Explanation:
|
We calculate the confidence interval for the
mean using Excel and we obtain the following results.
If we take 100 samples of employees from the
same population, the mean salary of the employees would lie between
59707.13 and 64905.13 in approximately 99 of the samples.
|
- Compare your answers for (2) and (3). You notice that the 99% confidence interval is wider. What is the advantage of using a wider confidence interval? Why would you not always use the 99% confidence interval? Explain with an example.
Answer
and Explanation:
|
The results from (2) and (3) shows that the 99%
confidence interval is wider. If we use wider confidence level, we have a
greater chance of obtaining a parameter within the interval every time we
sample from the same population. The 95% confidence interval, therefore,
would allow someone to be more confident that the true population parameter
is contained within that interval. For example if we were to compare the mean
IQ test scores of students from two
classes, it would be prudent to consider a 95% confidence interval
over a 99% confidence interval for
the difference in means so that we are more confident that there exists a
difference or not.
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- We want to estimate the mean salary in Minnesota. How many jobs must be randomly selected for their respective mean salaries if we want 95% confidence that the sample mean is within $126 of the population mean and σ = $1150.
Is
the current sample size of the data set in our excel document of 364 large
enough? Explain.
Answer
and Explanation:
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