Refer to Table 1 in the article “Snail Shells in a Practical Application of Statistical Procedures” in the Electronic Reserve Readings. Find the margin of error, E, with a confidence interval of your choosing (50-99%). What is the significance of choosing a confidence interval? What is the difference between selecting a 50% confidence interval versus a 95% confidence interval? What happens to E if the sample size is increased tenfold?
To find the margin of error (E) for a confidence interval in Table 1 of the article "Snail Shells in a Practical Application of Statistical Procedures," you need to choose a confidence level and then locate the corresponding margin of error in the table.
1. Start by choosing a confidence interval: The confidence interval is typically expressed as a percentage, ranging from 50% to 99%. You can choose any confidence level within this range.
2. After choosing the confidence interval, refer to Table 1 in the article to find the associated margin of error. The table should provide the desired confidence levels and their corresponding margins of error.
Now, let's discuss the significance of choosing a confidence interval and the difference between selecting a 50% and a 95% confidence interval:
1. Significance of choosing a confidence interval: A confidence interval represents the range of values within which an estimated population parameter is likely to fall. It provides a measure of the precision or reliability of the estimate. Choosing a confidence interval allows you to quantify the uncertainty associated with estimating the population parameter using sample data.
2. Difference between a 50% and a 95% confidence interval: The confidence level determines the percentage of confidence in the estimation. A 50% confidence interval implies that if you repeat the sampling process multiple times, around 50% of the intervals constructed would contain the true population parameter. On the other hand, a 95% confidence interval means that about 95% of the intervals constructed from repeated sampling would capture the true population parameter.
Next, let's discuss the effect of increasing the sample size tenfold on the margin of error (E):
Increasing the sample size has a direct impact on the margin of error. The margin of error (E) decreases as the sample size increases. With a larger sample size, you have more information about the population, which leads to more precise estimates. As a result, the margin of error decreases because the uncertainty associated with the estimation is reduced.
Therefore, if the sample size is increased tenfold, you can expect the margin of error (E) to be significantly smaller compared to the original value. This indicates that the estimate obtained with the larger sample size is more precise and provides a narrower range for the estimated population parameter.