If you wish to estimate a population mean with a sampling distribution error SE=0.34 using a​ 95% confidence interval and you know from prior sampling that sigma squared is approximately equal to 7.3​, how many observations would have to be included in your​ sample?


To estimate the required sample size \( n \) for a 95% confidence interval with a given standard error \( SE = 0.34 \) and a known population variance \( \sigma^2 = 7.3 \), we use the formula for the standard error of the mean:

\[
SE = \frac{\sigma}{\sqrt{n}}
\]

where:
- \( SE \) is the standard error,
- \( \sigma \) is the standard deviation of the population,
- \( n \) is the sample size.

Given that \( \sigma^2 = 7.3 \), we can calculate \( \sigma \) as:

\[
\sigma = \sqrt{7.3}
\]

Next, we rearrange the formula to solve for \( n \):

\[
n = \left( \frac{\sigma}{SE} \right)^2
\]

Substitute the given values:

\[
n = \left( \frac{\sqrt{7.3}}{0.34} \right)^2
\]

Let's compute the value of \( n \).The required sample size \( n \) to estimate the population mean with a standard error of 0.34 using a 95% confidence interval is approximately **63** observations (rounding up to the nearest whole number).

Would you like more details on this calculation or have any other questions?

Here are some related questions that might interest you:
1. How does the confidence level affect the required sample size?
2. What is the relationship between standard error and standard deviation?
3. How do you interpret a confidence interval in statistics?
4. What happens if the population variance is unknown?
5. How would the required sample size change if the standard error were different?

**Tip:** Always round up when calculating sample size, as partial samples are not practical in statistics.

If you wish to estimate a population mean with a sampling distribution error SE=0.34 using a​ 95% confidence interval and you know from prior sampling that sigma squared is approximately equal to 7.3​, how many observations would have to be included in your​ sample?

Learn how to calculate the sample size needed to estimate a population mean with a 95% confidence interval and a standard error of 0.34. The problem involves known population variance (7.3) and uses key statistical concepts like sampling distribution and confidence intervals. Ideal for undergraduate students studying statistics.

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