Statistics: Confidence Intervals

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Discussion Overview

The discussion centers around calculating the margin of error for a confidence interval using given values of confidence level (c), sample standard deviation (s), and sample size (n). Participants explore how to find the corresponding zc value for a confidence level of c=0.65, which is not provided in a standard chart.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents a problem involving the calculation of the margin of error using the formula E = (zc s) / n^.5, noting the absence of a zc value for c=0.65 in the provided chart.
  • Another participant claims that zc=0.93 for c=0.65, suggesting it can be found in the Standard Normal Distribution table.
  • A third participant questions how the zc value of 0.93 is determined and expresses interest in deriving a table independently.
  • A later reply suggests that numerical integration of the normal distribution's probability density function (pdf) could be a straightforward method to find zc, while also mentioning the error function as a more traditional but complex approach.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method to derive the zc value for c=0.65, with differing opinions on the approach to take and the validity of the proposed zc value.

Contextual Notes

There is uncertainty regarding the derivation of the zc value for c=0.65, and the discussion includes various methods that may or may not be accessible to all participants.

Phrynichos
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The problem in question is as follows:

Find themargin of error for the given values of c, s, and n. where c is the confidence interval, s is the sample standard deviation and n is the number of objects.

c=0.65 s= 1.5 n=50

the formula: E= (zc s) / n^.5

Level of Confidence Chart

c ......zc
.80......1.28
.90......1.645
.95......1.96
.99.....2.575


As you can see, the zc value for c=.65 is not present on the chart. I don't know how to proceed to solve the problem by finding the corresponding zc for when c=.65. if anyone could show me, that would be appreciated.
thankx
 
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z_{c}=0.93 for c=0.65. Easy to find on your table for the Standard Normal Distribution.
 
Hey LearnFrench,

How do they determine the 0.93 statistic in the first place? Assuming I have no life, how could I derive a table on my own?

Thanks,
HF08
 
Numerical integration of the normal distribution's pdf would probably be the easiest way. The more traditional but also more complex way would start with the error function.
 

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