Question

===================================================================================== Problem 3. (2pts) The graph below shows the results from constructing 100 different confidence intervals of the same confidence level, each based on a different sample of size from a population in which the population mean is u = 20. Each vertical line in the graph spans the length of a different confidence interval. 100 40 60 Sample Number Based on these results, what is the most likely value of the confidence level used in constructing these confidence intervals?

Answer 1

The C% confidence interval for the population mean is interpreted as if there are repeated samples and confidence interval is computed for each sample then out of 100, C times confidence interval will contain the actual population mean value. So if we have 95% confidence interval it means if we draw 100 samples then at least 95 samples contain the actual population mean value into the confidence interval.

Now here we have a population mean value 20 and 100 confidence intervals are computed. So first we will see how many confidence intervals does not contain the actual population mean value.

Now from the graph we can see the 4th confidence interval and 24th confidence interval does not contain the population mean value. It means 2 confidence intervals does not contain population means value.

So out of 100, 98 confidence intervals contain the population mean. So, in other words, we can say here we are 98% confident. It means most likely used confidence level value in constructing confidence intreval is 0.98