Confidence Level
Because you used 0.05 as the cut-off value in determining the plausible values, we call the interval of plausible values you just found a 95% confidence interval. Here, 95% is the confidence level, and provides a measure of the reliability of our method. Our interpretation is that we are 95% confident that the probability a kissing couple turns right is inside the interval.
(j) Calculate the midpoint of your interval by averaging the two endpoints. Does this value seem familiar? Why does that make sense?
(k) Calculate the half-width of your interval by subtracting the endpoints and dividing by two.
| This value is often referred to as the margin-of-error and many confidence intervals have the form estimate + margin-of-error, where the margin-of-error measures the accuracy of our statistic, how close we think we are to the actual parameter value. |
(l) Suppose we used 0.01 as the cut-off value instead. Use the table you created in (i) to determine the interval of plausible values. What is the corresponding confidence level? Write a sentence interpreting this interval in context.
(m) How did the margin-of-error change when we changed the confidence level? Explain why this change makes sense intuitively.
