5588> Modules> Week 6: Confidence Interval Concepts This is a graded discussion:

Question

5588> Modules> Week 6: Confidence Interval Concepts This is a graded discussion: 10 points possible due Apr 8 64 Week 6: Confidence Interval Concepts Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you nfidenceI A. increase the co B. increase the sample size, or C. increase the margin of error? Only consider one of these changes at a time. Explain your and by referencing the formula. Unread Subscribe Search entries or author Reply

Explanation / Answer

a) If we increase the confidence level, the confidence interval becomes wider. If you increase your confidence level, alpha decreases and your z-value (or whatever distribution you're taking from) increases so you have a larger error. More error means a larger confidence interval.

b) If you increase sample size, the confidence interval becomes smaller because your error becomes smaller. Recall that the larger your sample size, the more you decrease error and the more likely you are to get a better approximation of the true population parameter.

C) margin of error = Zcritical * ( standard error )

Where standard error = standard deviation / ?(sample size)

As sample size increases, the margin of error decreases. As the variability in the population increases, the margin of error increases. As the confidence level increases, the margin of error increases.

If we increase the margin of error, the confidence level will increase. Since the Confidence interval = point estimate +/- margin of error. As the second component gets bigger, the width of the confidence interval will also get bigger.

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