Based On The Class Sample, You Will Create A 95% Confidence

Question

Based on the class sample, you will create a 95% confidence Based on the class sample, you will create a 95% confidence interval for the mean age and the proportion of males in the population of all online college students. Note: The goal of the project is to practice making a confidence interval for a mean and proportion with real data. Do not worry about failed assumptions tests and do not make corrections for small sample size. Use primary methods described in text and used on homework. Using the same excel sheet as last week, answer the following in the “week 5” tab: For the average age, form a 95% confidence interval: What distribution should be used? What is the critical value? What is the error bound? What is the lower bound? What is the upper bound? How do we interpret the results, in context of our study? For the proportion of males, form a 95% confidence interval: What distribution should be used? What is the critical value? What is the error bound? What is the lower bound? What is the upper bound? How do we interpret the results, in context of our study?

Dr. Jack HW Helper · Accepted Answer

The creation of confidence intervals is an essential aspect of statistics that allows researchers to estimate population parameters based on sample data. In this paper, we will calculate a 95% confidence interval for the mean age of online college students as well as the proportion of males in this population. We will employ primary methods as discussed in the course material. Confidence Interval for Mean Age Distribution to Use: For estimating the mean age, we will use the t-distribution. This is appropriate when the population standard deviation is unknown, which is often the case with sample data. The t-distribution is particularly useful for smaller sample sizes (typically n Critical Value: The critical value for a 95% confidence interval, when using the t-distribution, can be determined from the t-table. For this instance, assuming we have a sample size of $ n = 30 $, with $ n - 1 = 29 $ degrees of freedom, the critical t-value (two-tailed) is approximately 2.045. Error Bound: The error bound, also known as the margin of error (E), is calculated using the formula: E = t^* (s/√n) Where $ t^* $ is the critical value, $ s $ is the sample standard deviation, and $ n $ is the sample size. For example, if the sample standard deviation $ s $ is 5 years and the sample size $ n $ is 30, the calculation would be: E = 2.045 * (5 / √30) ≈ 1.87 years. Lower Bound: The lower bound of the confidence interval can be calculated using the formula: Lower Bound = $ \bar{x} - E $ Assuming the average age $ \bar{x} $ is 25 years, the lower bound would be: Lower Bound = 25 - 1.87 ≈ 23.13 years. Upper Bound: The upper bound is calculated similarly: Upper Bound = $ \bar{x} + E $ Upper Bound = 25 + 1.87 ≈ 26.87 years. Interpretation: The interpretation of the 95% confidence interval for the mean age, which ranges from approximately 23.13 years to 26.87 years, means that we are 95% confident that the true mean age of all online college students falls within this inter

Based On The Class Sample, You Will Create A 95% Confidence ✓ Solved

Based on the class sample, you will create a 95% confidence

Paper For Above Instructions

Confidence Interval for Mean Age

Confidence Interval for Proportion of Males

Conclusion

References