The distribution of heights of 18-year-old men in the United States is approxima

Question

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 size 20 from this population (right double arrow implies Calc right double arrow implies Random Data right double arrow implies Normal, with 20 rows from a distribution with mean 68 and standard deviation 3). Then we can have Minitab compute a 95% confidence interval and draw a boxplot of the data (right double arrow implies Stat right double arrow implies Basic Statistics right double arrow implies 1 -- Sample t, 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 N MEAN STDEV SEMEAN 95.0 % CI Sample 1 20 68.050 2.901 0.649 (66.692 , 69.407) Sample 2 20 67.958 3.137 0.702 (66.490 , 69.426) Sample 3 20 67.976 2.639 0.590 (66.741 , 69.211) Sample 4 20 66.908 2.440 0.546 (65.766 , 68.050) (a) Examine the figure [parts (a) to (d)]. How do the boxplots for the four samples differ? Why should you expect the boxplots to differ? They differ in interquartile length, median location, and whisker length. The boxplots differ because they come from the same sample. They differ in interquartile length and median location. The boxplots differ because they come from different samples. They differ in interquartile length and whisker length. The boxplots differ because they come from different samples. They differ in interquartile length, median location, and whisker length. The boxplots differ because they come from different samples.

Explanation / Answer

the samples are random so if we again generates the sample of 20 from the normal population the sample will differ and hence boxplot and 95% confidence interval(CI). so for simplicity we are following the 95% CI provided in question.

(a) Examine the figure [parts (a) to (d)].

95.0 % CI

Sample 1 (66.692 , 69.407)

Sample 2 (66.490 , 69.426)

Sample 3 (66.741 , 69.211)

Sample 4 (65.766 , 68.050)

How do the boxplots for the four samples differ?

boxplot will differ as because of randomness of sample the 1st sample is (66.692 , 69.407) and the 2nd one is (66.490 , 69.426) so the 1st boxplot will contain the 2nd boxplot. and son on with same comparison for the others.

Why should you expect the boxplots to differ?

because of the randomness the samples will comes around mean with given standard deviation. Now a sample we get less scatter comarison to the mean then we get the shorter interval of 95% CI (2nd sample). If the scatterness of the data increses then will get a wider interval of 95% CI(1st case)

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