1. Discuss confidence levels and make decision we are using the mean as the base
ID: 3228968 • Letter: 1
Question
1. Discuss confidence levels and make decision we are using the mean as the bases for our central point. Why are we able to do this and what are some of the parameters we must consider? 2. Discussed confidence levels in Chapter 9 and Hypothesis testing in Chapter 10. What are the common elements of each? When would you use one or the other? 3. Explain when you would use the “z” table to determine distance from the center point on the curve and when you would use the “t” table? 4. Explain what is meant by the sampling error?
Explanation / Answer
A confidence interval is a range of values that is likely to contain an unknown population parameter. If you draw a random sample many times, a certain percentage of the confidence intervals will contain the population mean. This percentage is the confidence level.
The confidence level is not the probability that a specific confidence interval contains the population parameter.
The confidence level represents the theoretical ability of the analysis to produce accurate intervals if you are able to assess many intervals and you know the value of the population parameter.
There is an extremely close relationship between confidence intervals and hypothesis testing. When a 95% confidence interval is constructed, all values in the interval are considered plausible values for the parameter being estimated. Values outside the interval are rejected as relatively implausible. If the value of the parameter specified by the null hypothesis is contained in the 95% interval then the null hypothesis cannot be rejected at the 0.05 level. If the value specified by the null hypothesis is not in the interval then the null hypothesis can be rejected at the 0.05 level.
Hypothesis testing relates to a single conclusion of statistical significance vs. no statistical significance.
Confidence intervals provide a range of plausible values for your population.
Use hypothesis testing when you want to do a strict comparison with a pre-specified hypothesis and significance level.
Use confidence intervals to describe the magnitude of an effect or when you want to describe a single sample.
When the distribution is normal and population variance is known, we use Z table.
When the distribution is approximately normal and the sample size is small and population variance is not known, we use t table.
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