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## BIO 500 W4 Confidence Interval Essay

*BIO 500 W4 Confidence Interval Essay*

**Details:**

In the Topic 1 Assignment, you compared the BMI values from Data Set 1 (in the appendix of the textbook) from a perspective of measuring the center and variation of the data. Chapters 5 and 6 in the textbook allow you to use more sophisticated tools to estimate the parameters of a population.

Refer to Data Set 1 in Appendix B and use the sample data with Excel and/or SPSS to accomplish the following:

Construct a 99% confidence interval estimate of the mean body mass index for men.

Construct a 99% confidence interval estimate of the mean body mass index for women.

Compare and interpret the results. It is known that men have a mean weight that is greater than the mean weight for women, and the mean height of men is greater than the mean height of women. Do men also have a mean body mass index that is greater than the mean body mass index of women?

APA format is not required, but solid academic writing is expected.

This assignment uses a grading rubric. Instructors will be using the rubric to grade the assignment; therefore, students should review the rubric prior to beginning the assignment to become familiar with the assignment criteria and expectations for successful completion of the assignment.

You are not required to submit this assignment to Turnitin.

In statistics, a **confidence interval** (**CI**) is a type of estimate computed from the observed data. This gives a range of values for an unknown parameter (for example, a population mean). The interval has an associated **confidence level** chosen by the investigator. For a given estimation in a given sample, using a higher confidence level generates a wider (i.e., less precise) confidence interval. In general terms, a confidence interval for an unknown parameter is based on sampling the distribution of a corresponding estimator.^{[1]}

This means that the confidence level represents the theoretical long-run frequency (i.e., the proportion) of confidence intervals that contain the true value of the unknown population parameter. In other words, 90% of confidence intervals computed at the 90% confidence level contain the parameter, 95% of confidence intervals computed at the 95% confidence level contain the parameter, 99% of confidence intervals computed at the 99% confidence level contain the parameter, etc.^{[2]}

The confidence level is designated before examining the data. Most commonly, a 95% confidence level is used.^{[3]} However, other confidence levels, such as 90% or 99%, are sometimes used.

Factors affecting the width of the confidence interval include the size of the sample, the confidence level, and the variability in the sample. A larger sample will tend to produce a better estimate of the population parameter, when all other factors are equal. A higher confidence level will tend to produce a broader confidence interval.

Another way to express the form of confidence interval is a set of two parameters: *(point estimate – error bound, point estimate + error bound)*, or symbolically expressed as *(–EBM, +EBM)*, where (point estimate) serves as an estimate for *m* (the population mean) and EBM is the error bound for a population mean.