Finding sample size given info on confidence interval

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Homework Help Overview

The discussion revolves around determining the appropriate sample size for estimating a population mean within a specified margin of error and confidence level. The context involves a population believed to be bounded between 38 and 70, with a focus on statistical concepts related to confidence intervals and variance.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formula for the variance of the sampling distribution and express uncertainty regarding the population variance. Some explore the implications of assuming a uniform distribution of values between the given bounds, while others suggest using the three standard deviation rule to estimate standard deviation.

Discussion Status

The discussion is active with participants questioning the assumptions about the population variance and exploring different interpretations of the data provided. Some guidance has been offered regarding the use of the three standard deviation rule, but no consensus has been reached on the exact approach to take.

Contextual Notes

There is a noted lack of explicit information regarding the population variance, which is central to solving the problem. Participants are also considering the implications of the range of values provided in the context of their calculations.

eterna
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Homework Statement



Suppose that an investigator believes that virtually all values in the population are between 38 and 70. The appropriate sample size for estimating the true population mean within 2 units with 95% confidence level is approximately how much?

Homework Equations

Variance of the sampling distribution of size n = Variance of the population distribution / n

The Attempt at a Solution

I think I'm solving
1.96(SD of the sampling distribution of size n)=2

But I don't think there's any information given on the population variance so I don't know what to do.
 
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Worst case, half the population values are 38 and half are 70. What's the variance in that case?
 
eterna said:

Homework Statement



Suppose that an investigator believes that virtually all values in the population are between 38 and 70. The appropriate sample size for estimating the true population mean within 2 units with 95% confidence level is approximately how much?

Homework Equations




Variance of the sampling distribution of size n = Variance of the population distribution / n

The Attempt at a Solution




I think I'm solving
1.96(SD of the sampling distribution of size n)=2

But I don't think there's any information given on the population variance so I don't know what to do.

Use the three standard deviation rule.
 

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