phase 5 project

Running head: INFECTIOUS DISEASES – PHASES 2 0

Project Phase 2 – Scenario 2

Author Note

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Infectious Diseases

What are Confidence Intervals?

Confidence intervals are a range of values that have acquired a definition and have a particular probability that the value that a parameter is able to attain lies within this range. A confidence interval exists to indicate the level of precision in a measurement made (Cumming, 2012). A point estimate is a single value that exists as an estimate of a population parameter calculated from the sample data of a population.

The best point estimate for the population mean is the mean obtained from the sample calculated as the average. The reason is because the sample mean has the characteristics of being unbiased as an estimate of the mean of the population (Cumming, 2012). Confidence intervals are important because having considered the size of the sample and the variations that lie in this sample potentially; they produce an estimate in which the real answer can be found. Confidence intervals introduce the potential for risks in decision making. Risks are increased when confidence intervals are underestimated. They give a picture of how accurate or precise an estimate is.

From the sample in the excel sheet g310, the total is 3709 while the sample mean is 61.8166 The sample mean is not the same as the population mean but it is a good point estimate for the population mean. The standard deviation of the sample is 8.92433. The Z-value is 0.41953.

Confidence interval

= CI for sample mean with unknown  = /x */ t* s/60 = 1.8167 +/ 0.41953 * 8.92433/60 = 61.3334 or 62.3

Following the calculation of the confidence interval for the mean, the values obtained as the mean of the population will lie between the values 61.3334 and 62.3. The values give a range in which to expect the value of the mean of the population. The values are just but a risk. This is an expectation of the outcome in case of anything but things may turn out to be different from what has been obtained. The confidence interval in this case ranges from 61.3334 to 62.3 in which the sample mean is included. The sample mean is the midpoint of the two values that give the confidence interval. This is part of reason why the sample mean is referred to as the best point estimate of the population mean.

Shifting the confidence intervals from 95% to 99% leads to a change in the standard deviation because all other variables are constant in this case. This change means that there is a reduction in risk as one increase the confidence interval. An increase in confidence interval means a subsequent increase in the standard deviation of the sample and a reduction in risk level. A reduction in confidence interval means a subsequent reduction in the standard deviation and an increment in the level of risk.

Conclusion

The confidence interval is designed to give a range of values where an estimate value is supposed to fall. The mean of the sample is the best value for use as a point estimate. It occurs as the midpoint of the two values that provide the range in which the actual value may fall. Reducing the value of confidence interval increases the risk of falling outside the interval. This means that the likelihood of obtaining the actual value reduces. On the other hand, increasing the confidence interval increases the probability of obtaining the actual value and reduces the risk of not doing so.

Reference

Cumming, G. (2012). Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis. New York: Routledge.