A POLL OF 1300 RANDOMLY SELECTED STUDENTS IN GRADES 6 THROUGH-8 WAS CONDUCTED AND FOUND THAT 54% ENJOY PLAYING SPORTS. WOULD CONFIDENCE IN THE RESULTS INCREASE IF THE SAMPLE SIZE WERE 3000 INSTEAD OF 1300? WHY OR WHY NOT?
First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.
Standard Error of the mean (SEm) = SD/√n, so when n increases, SEm is reduced.
To analyze whether confidence in the results would increase if the sample size were 3000 instead of 1300, we need to understand the concept of sample size and its relationship to confidence.
In statistics, sample size refers to the number of individuals or data points included in a study or survey. A larger sample size generally leads to more reliable and precise results because it provides a better representation of the population being studied.
One way to evaluate the precision or confidence in survey results is through the concept of margin of error. The margin of error indicates how much the sample estimate may vary from the true population value. A smaller margin of error is desirable as it suggests higher confidence in the results.
To calculate the margin of error, we need to consider factors such as sample size, level of confidence, and the estimated proportion.
In this case, the sample size is 1300, and the estimated proportion of students enjoying playing sports is 54%. If we increase the sample size to 3000, the margin of error is expected to decrease, resulting in a higher level of confidence in the survey results.
For example, a larger sample size reduces the variability and uncertainty associated with estimating the proportion of students who enjoy playing sports. As a result, the survey results will likely have a narrower margin of error, increasing confidence in the findings.
Therefore, in general, increasing the sample size from 1300 to 3000 would likely improve the confidence in the survey results by reducing the margin of error and providing a more accurate estimate of the proportion of students who enjoy playing sports.