1 For this question refer to the figure below or to the hand

1. For this question refer to the figure below (or to the handout CI-Simulation), which displays two separate plots. Below arc a few bullet points to describe the plots. . Each of the two plots display 100 confidence intervals. . Every confidence interval is visualized as a single vertical Iliac where the circles at the beginning and end indicate the lower and upper hound of the interval, respectively. . Within each plot, all confidence intervals are of the same confidence level and same sample size, n; both are specified in the title of the graph. However, each interval is based on a different random sample. . The horizontal line in bold in the middle of each plot represents the population mean ,mu that we are trying to predict. (Note that in general mu will he unknown to us.) . Confidence intervals that contain the population mean mu are shown in plain lines. . Confidence intervals that do not contain the population mean mu are shown in bold lines. (a) According to the long-run behavior of the confidence interval procedure out of 100 confidence intervals, how many should you expect to not contain the population mean if these are 95% confidence intervals? (b) How many of the confidence intervals do not actually contain the population mean in the confidence interval simulation \'\'95% with n=30? (c) How many of the confidence intervals do not actually contain the population mean in the confidence interval simulation \'\'95% with n= 120?\'\' (d) When I increase my sample size, my confidence intervals become precise! (Fill in the blank with either More or Less.)

Solution

a). We expect 5 intervals do not contain population mean b). 4 intervals actually do not contain population mean a). 6 intervals actually do not contain population mean d). More