What Factors Affect the Margin of Error? (In a Confidence Interval for One Mean)
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- เผยแพร่เมื่อ 15 ก.ย. 2024
- A look at the effect of various factors (the standard deviation, the sample size, and the confidence level) on the margin of error of a confidence interval for the population mean.
For those that use R, below I give the R code to find the values given in this video.
Z value for a 90% interval (see my other videos for a more detailed explanation of the rationale):
qnorm(.95)
[1] 1.644854
Z value for a 95% interval:
qnorm(.975)
[1] 1.959964
Z value for a 99% interval:
qnorm(.995)
[1] 2.575829
Thanks for the compliment! I'm very glad they helped you learn a little statistics! By "critical values for Z" are you referring to the appropriate z value for the interval formula, or the critical z value for a hypothesis test? For the confidence interval, I have a video "Finding the Appropriate z Value for the Confidence Interval Formula" at th-cam.com/video/grodoLzThy4/w-d-xo.html, and for hypothesis testing I have the video "$Z$ Tests for One Mean: The Rejection Region Approach" at th-cam.com/video/60x86lYtWI4/w-d-xo.html.
You don't get that by a formula. It comes from integrating the standard normal pdf, but that doesn't have a closed form solution. So in practice we use either software or a table. I walk through examples of using the table in the video I referred to in my earlier reply. Cheers.
Thank you Prof Balka, as ever, for your straight to the point videos - the importance of remembering that confidence intervals relate to the estimation of a parameter and not of a statistics is too often left out from the discussion, even in my graduate course!!
I just wanted to say, I love your videos! You've really helped me understand margin of error. The only thing I'm a little confused about is how to find the Critical Values for Z.
Excellent! Thanks, these really help! Can I just clarify, the smaller the margin of error means the more precise is the estimate? Is it true? Thanks..
I will definitely have to watch that then! Thank you so much!
What I was having a hard time understanding was the Z critical value, for say 90%. I know that 90% is 0.90 so 1 - 0.90 = 0.10 then you divide 0.10/2 which is the a/2 part to give you 0.05. What i don't understand is the inverse norm of that to give you the Critical value of 1.645 for Za/2. (if that makes sense?) I'm not sure which formula is used to find 1.645.
Love the videos. Just wanted to clarify that you're only referring to zed values in two-sided intervals, not one-sided. The zed values will be different for one-sided.
Thanks! Yes, I'm referring to two-sided intervals. At the start, I state "suppose we use X bar +/- z...", indicating a two-sided interval.
@@jbstatistics Thank you! Appreciate the quick response! Your videos are earning me my grade.