Assignment: Confidence Interval

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Assignment: Confidence Interval

Assignment: Confidence Interval

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Confidence Interval for Population Mean:

sample mean – E < population mean < sample mean + E

Error “E” = (1.96)*(s) / sqrt(n)

“s” is the standard deviation and “n” is the sample size.

Part 1: Confidence Intervals

  1. Why is it often impossible to know the actual value of any population parameter? Give an example of a population parameter that you cannot calculate, but that you can estimate.
  2. A sample can be used to estimate a population parameter. How does the sample size affect the estimate? If the sample is larger, what will this do to the error E?
  3. Use the Confidence Interval formula above and calculate the 95% confidence interval for any population mean of your choice. Write down (invent) the sample size (be sure it is 30 or above), the sample mean, and the sample standard deviation. Then, calculate the confidence interval. Remember, you are inventing all the values, so no two posts should look the same.
  4. Use Excel and your invented values to calculate the confidence interval. Include and compare the results. Again, remember that your sample size must be 30 or above. Please show all calculations and give examples accordingly.
  5. Include reference from:  Bennett, Jeff, Briggs, W. L., Triola, M. F. (12/2012). Statistical Reasoning for Everyday Life, 4th Edition.

In , a confidence interval (CI) is a type of , computed from the statistics of the observed data, that might contain the true value of an unknown . The interval has an associated confidence level, or coverage that, loosely speaking, quantifies the level of confidence that the deterministic parameter is captured by the interval. More strictly speaking, the confidence level represents the frequency (i.e. the proportion) of possible confidence intervals that contain the true value of the unknown population parameter. In other words, if confidence intervals are constructed using a given confidence level from an infinite number of independent sample statistics, the proportion of those intervals that contain the true value of the parameter will be equal to the confidence level.

Confidence intervals consist of a range of potential values of the unknown . However, the interval computed from a particular sample does not necessarily include the true value of the parameter. Based on the (usually taken) assumption that observed data are random samples from a true population, the confidence interval obtained from the data is also random.

The confidence level is designated prior to examining the data. Most commonly, the 95% confidence level is used. However, other confidence levels can be used, for example, 90% and 99%.

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.

Confidence intervals were introduced to statistics by  in a paper published in 1937

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