Changing either z, n or 1 in the margin of error will have different impacts on

Question

Changing either z, n or 1 in the margin of error will have different impacts on the overall width of a confidence interval O Change level of confidence C: this will change z* Increasing C (higher confidence) yields a larger z value and in turn a CI. CI Change sample size n: this will change /Vn Decreasing C (less confidence) yields a smaller z" value and in turn a · Increasing n (larger sample size) yields a smaller /vn value and in turn a CI ·Decreasing n (smaller sample size) yields a larger /vn value and in turn a CI O Change (assuming this can happen): this will change Increasing (larger population standard deviation) yields a larger value and in turn a CI ·Decreasing (smaller population standard deviation) yields a smaller /v n value and in turn a CI "Note that changing is rarely a feasible option Fall 2017, Stat 226 (Sections L) Introduction to Statistics Module 5, Chapter 15 26 28 Before we move on, let's revisit two major concepts of confidence intervals o Interpretation of Confidence Intervals Data Assumptions Interpretation of Confidence Intervals Referring to the handout on the 100 simulated confidence intervals we can take a away the following facts We can be that the falls inside the constructed level C confidence interval, i.e. between the lower and upper bound of the CI for a specific calculated example If we were to take repeated samples, in the long run, approximately will include the O The interpretation of a Cl is always in terms of the unknown population mean and never in terms of the sample mean x. The sample mean X, the center of every CI, will always be included in the Cl Fall 2017, Stat 226 (Sections L) Introduction to Business Statistics Module 5, Chapter 15 27/28

Explanation / Answer

1. Increasing C yields a larger Z value and in turn a INCREASE CI
Decreasing C yields a larger Z value and in turn a Decrease CI

2. Increasing n yields a smaller sigma/sqrt(n) value and in turn a Decrease CI
Decrease n yields a smaller sigma/sqrt(n) value and in turn a increase CI

3. Increase
Decrease

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