Finding sample size given info on confidence interval

In summary, the appropriate sample size for estimating the true population mean within 2 units with 95% confidence level, given that virtually all values in the population are between 38 and 70, is approximately half the population size. To calculate the standard deviation, use the three standard deviation rule.
  • #1
eterna
19
0

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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  • #2
Worst case, half the population values are 38 and half are 70. What's the variance in that case?
 
  • #3
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.
 
  • #4

1. How is the sample size determined for a given confidence interval?

The sample size is determined by considering three factors: the desired confidence level, the margin of error, and the population size. These factors are used to calculate the necessary sample size using a formula or a sample size calculator.

2. Why is it important to determine the appropriate sample size for a confidence interval?

Determining the appropriate sample size is important because it affects the accuracy and precision of the results. A small sample size may not be representative of the population, leading to inaccurate conclusions. On the other hand, a large sample size can be costly and time-consuming, so finding the appropriate size is crucial.

3. How does the confidence level affect the sample size?

The confidence level, also known as the confidence coefficient, is the probability that the true population parameter falls within the given confidence interval. The higher the confidence level, the wider the interval, and therefore, the larger the sample size needed to achieve the desired level of precision.

4. Can the sample size be determined after collecting the data?

In most cases, the sample size needs to be determined before collecting the data. However, if the initial sample size was too small, additional data can be collected and used to recalculate the sample size to achieve the desired confidence level and margin of error.

5. How does the margin of error influence the sample size?

The margin of error is the maximum amount of error allowed in the estimate of the population parameter. A smaller margin of error requires a larger sample size, while a larger margin of error allows for a smaller sample size. This is because a larger sample size leads to a more precise estimate of the population parameter.

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