We appreciate your visit to A sample of 40 chipmunks taken from a park in Owensboro has a mean mass of 461 7 g with a standard deviation of 97. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the margin of error for the mean mass of all the chipmunks in the park with a 94% confidence interval, you can follow these steps:
1. Understand the given data:
- Sample size ([tex]\( n \)[/tex]) = 40
- Sample mean = 461.7 grams (not needed for margin of error)
- Sample standard deviation ([tex]\( s \)[/tex]) = 97.9 grams
- Confidence level = 94%
2. Determine the critical value (z-value):
- Since the confidence level is 94%, you need to find the z-value that corresponds to the central 94% of the standard normal distribution.
- This involves looking up the z-value for the cumulative probability of [tex]\( \frac{1 + 0.94}{2} = 0.97 \)[/tex].
- The z-value for 0.97 is approximately 1.8808.
3. Calculate the standard error:
- The standard error (SE) is determined by dividing the sample standard deviation by the square root of the sample size:
[tex]\[
\text{SE} = \frac{\text{sample standard deviation}}{\sqrt{\text{sample size}}} = \frac{97.9}{\sqrt{40}} \approx 15.4793
\][/tex]
4. Calculate the margin of error (E):
- Multiply the z-value by the standard error to find the margin of error:
[tex]\[
E = z \times \text{SE} = 1.8808 \times 15.4793 \approx 29.1135
\][/tex]
Therefore, the margin of error is approximately 29.1135 grams when rounded to four decimal places.
1. Understand the given data:
- Sample size ([tex]\( n \)[/tex]) = 40
- Sample mean = 461.7 grams (not needed for margin of error)
- Sample standard deviation ([tex]\( s \)[/tex]) = 97.9 grams
- Confidence level = 94%
2. Determine the critical value (z-value):
- Since the confidence level is 94%, you need to find the z-value that corresponds to the central 94% of the standard normal distribution.
- This involves looking up the z-value for the cumulative probability of [tex]\( \frac{1 + 0.94}{2} = 0.97 \)[/tex].
- The z-value for 0.97 is approximately 1.8808.
3. Calculate the standard error:
- The standard error (SE) is determined by dividing the sample standard deviation by the square root of the sample size:
[tex]\[
\text{SE} = \frac{\text{sample standard deviation}}{\sqrt{\text{sample size}}} = \frac{97.9}{\sqrt{40}} \approx 15.4793
\][/tex]
4. Calculate the margin of error (E):
- Multiply the z-value by the standard error to find the margin of error:
[tex]\[
E = z \times \text{SE} = 1.8808 \times 15.4793 \approx 29.1135
\][/tex]
Therefore, the margin of error is approximately 29.1135 grams when rounded to four decimal places.
Thanks for taking the time to read A sample of 40 chipmunks taken from a park in Owensboro has a mean mass of 461 7 g with a standard deviation of 97. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
