Summarize what you have learned about confidence intervals from the two articles above. Confidence intervals are powerful tools to test the assumptions of any test on means or proportions. The constructed interval shows that we are of at least a level of confidence that this interval contains the true value of the parameter of interest. Confidence intervals can be narrow or wide depending on the confidence level, the sample means, and computed variation. A narrower interval is better since its bounds are closer to the sample mean. Furthermore, confidence intervals are not only used in testing a single population, but also in testing the difference between two population parameters. It can be done by using two confidence intervals and checking if these intervals intersect at a point, denoting the absence of a significant difference. However, a more efficient way is to create a confidence interval for the difference in the parameter of the two populations. With that, we check the created interval if it contains the value zero which indicates no significant difference. Discuss why it would be important to find the population mean of the data used for this term. The population mean of the data denotes the true value of the population parameter - the one we are trying to estimate. Knowing the true value helps us assess the accuracy of our created interval. We can evaluate if the computed interval covers the true population value and at the same time we can also adjust the confidence level such that we assign the highest confidence level that still covers this true value. With all that, we can create an interval with the narrowest width and highest confidence. Provide a description of the data you were provided and discuss what you know about the chosen topic. The 80% confidence interval computed for this topic is [22.950, 29.450] This means that we are 80% confident that the true value of the parameter being estimated is within the range 22.950 and 29.450. 27 21 6 J 54 5 3 49 6 39 7 37 46 46 38 27 47 43 52 31 52 57 22 29 47 10 13 37 12 11 4 13 29 8 54 26 31 35 10 6 19 22 4 12 59 11 6 49 121. Use the table above to create an 80%, 95%, and 99% confidence interval. 2. Choose another confidence level (besides 80%, 95% or 99%) to create another confidence interval. Sample Size n - 50 Sample Mean - x - EX - 26.2000 Sample Standard Deviation = s = \\(E(X- x )/(n-1) ) = 17.68777 80% Level of Significance , a = 0.2 degree of freedom= DF=n-1= 49 't value-' ta/2- 1.299 [Excel formula =tiny(a/2.df) ] Standard Error , SE = s/Vn = 17.6878/150- 2.5014 margin of error , E-t*SE = 1.299*2.5014- 3.24953 Confidence interval is Interval Lower Limit = x - E = 26.2-3.2495- 22.95047 Interval Upper Limit = x + E = 26.2+3.2495- 29.44953 80% Confidence interval is (22.95