Confidence intervals are often misinterpreted and commonly confused with the pro

Question

Confidence intervals are often misinterpreted and commonly confused with the probability that something is likely to happen. In this journal, you have the opportunity to explore your understanding of these concepts. (Write one to two paragraphs)

Prompt: For each journal entry, the following critical elements must be met: Fulfills all requirements in the individual prompt Provides relevant application of course concepts Supports ideas and observations with examples from personal or professional situations Guidelines for Submission: Each journal entry should be 1 to 2 paragraphs in length and should be submitted through the Blackboard journal tool. Instructor Feedback: This activity uses an integrated rubric in Blackboard. Students can view instructor feedback in the Grade Center. For more information, review these instructions. Critical Elements Exemplary (100%) Proficient (85%) Needs Improvement (55%) Not Evident (0%) Value Prompt Meets “Proficient” criteria and references course materials Response meets all elements outlined in the prompt Response meets only some of the elements in the prompt Response does not meet the elements in the prompt 20 Course Concepts Meets “Proficient” criteria and supports response with course materials Clearly relates course concepts to the applicable journal prompt Relates course concepts to the applicable journal prompt, but response lacks clarity Does not relate course concepts to the applicable journal prompt 30 Personal or Professional Situations Meets “Proficient” criteria and further relates personal or professional circumstances to scholarly research Logically supports ideas and observations with examples from personal or professional circumstances or experiences Supports ideas and observations with examples from personal or professional circumstances or experiences, but response lacks logic Does not support ideas and observations with examples from professional circumstances or experiences 30

Explanation / Answer

Many users of statistics have argued that confidence intervals may in certain circumstances be
preferable to hypothesis testing (Gardner & Altman, 1986; Nakagawa & Cuthill, 2007), although
others have disagreed (Poole, 1987). A confidence interval is a way of describing the reliability of
an estimate. A statistician may be interested in the mean (or some other measure) of a population
but, except in rare cases, data will not be available for the entire population and a sample must
be taken instead. When the mean is calculated from a sample, it is unlikely to match precisely
the mean of the entire population, but it can be used as an estimate of the (unknown) population
mean. How good an estimate it is will depend on the size of the sample: other things being equal,a bigger sample will give a better estimate for the population mean. Specifying a confidence
interval is more informative than just giving the sample mean, because it provides a band of
values either side of the sample mean. A 95% confidence interval would have a wider band than
a 90% confidence interval for the same data, because the more certain you wish to be about
capturing the population mean, the less tightly you can set the limits. If you repeatedly use 95%
confidence intervals, then on 95% of occasions the population mean will be captured in your
interval—and one time in 20 it will lie outside it.

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