Question

.-/ pos t i27.2.019. The distribution of heights of 18-year-old men in the United States is approximately normal, with mean 68 inches and standard deviation 3 inches (U.S. Census Bureau). In Minitab, we can simulate the drawing of random samples of 20 from this population Calc Random Data Normal, with 20 rows from a distribution with means and standard deviation 3). Then we can have Minitab computea 95% confidence interval and draw a boxplot of the data (State Statistics 1 - Sample with boxplot selected in the graphs). The boxplots and confidence intervals for four different samples are shown in the accompanying figures. The four confidence intervals are as follows. VARIABLE TV (66.629.4071 Sample 2 20 67.958 3.137 0.102 166.430, 63.4261 Sample 67.916 0.550 Sample 6.546 (a) Examine the figure [parts (a) to (0) How do the boxplots for the four samples differ? Why should you expect the boxplots to differ? O They differ in interquartile length, median location, and whisker length. The bowplots differ because they come from different samples. They differ in interquartile length and whisker length. The bowplots differ because they come from different samples They differ in interquartile length, median location, and whisker length. The bowplots differ because they come from the same sample They differ in interquartile length and median location. The bowplots differ because they come from different samples. co m2 n ceal for the man d o 72 73 972 (b) Examine the confidence intervals for the four samples shown in the printout. Do the intervals differ in length? Do the intervals all contain the expected population mean of 68 inches? Select If we draw more samples, do you expect all of the resulting 95% confidence intervals to contain 687 Why or why not? o We expect all of the samples to generate intervals that contain the mean of the population We expect none of the samples to generate intervals that contain the mean of the population o we expect 95% of the samples to generate intervals that contain the mean of the population o we expects of the samples to generate intervals that contain the mean of the population Need Help?

Answer 1

a) From the 4 figures we can see that the IQR, the location of the median, the length of the whiskers all are different for these 4 samples. They differ because they come from different samples.

Hence option 1 is the correct one.

b) From the 4 figures we can see that confidence interval of all the 4 samples contains 68.

Hence we can expect 95% of the samples to generate intervals that contains the mean of the population.