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Exercise 7.3

1.
Consider the following simple data set.
           77     79     81     91    106    114    126    132
Obtain 5 resamples of this data set using the previous resampling code which we used for probability Click here for resampling code for probability modeling. (Just sample with replacement the numbers: min = 1, max = 8, trials = 5, numbers to be drawn 8. These are the sample item numbers for the resample. For example if the numbers you draw are:
      6       5       4       4       4       5       8       6
Then your resample is: 114, 106, 91, 91 91, 106, 132, 114

Obtain 4 more resamples. Calculate the median of each. Compare your resampled medians with the sample median.

2.
For the last problem use the class code One-Sample bootstrap means and medians (Sorted) to obtain a 95% confidence interval for the true population median based on 100 resamples.
3.
For problem #1, use the class code  One-Sample CI's for the mean and median to obtain a 95% confidence interval for the true population median based on 1000 resamples. Dotplot your data set and locate the confidence interval and sample median on your plot.
4.
Below are the weights of the pitchers in Carrie's baseball data set. Obtain the sample median. Use the class code One-Sample CI's for the mean and median to obtain a 95% confidence interval for the true population median weight of a professional baseball pitcher based on 1000 resamples. Locate your interval on the dotplot plot below and interpret your interval.
          160    175    180    185    185    185    190    190    195    195    195
          200    200    200    200    205    205    210    210    218    219    220
          222    225    225    232



                                     .      .  :
                     .         .  .  :   :  :  :   :  :    .... :    .
                 -------+---------+---------+---------+---------+---------C21
                      165       180       195       210       225       240
5.
Do the last problem for the weights of the hitters:
          155    155    160    160    160    166    170    175    175    175    180
          185    185    185    185    185    185    185    190    190    190    190
          190    195    195    195    195    200    205    207    210    211    230

                                       .
                                       :   .
                       .         .     :   :  :
                   :   :   . .   :  .  :   :  :  .   .. ..           .
                +---------+---------+---------+---------+---------+-------C22
              150       165       180       195       210       225
6.
Plot your CI's for the last two problems on the same real number line. What do you conclude about the true median weights of hitters and pitchers based on this plot?
7.
Select one of your textbooks or a novel that you are reading. Select a passage at random (not dialogue). Then count up the number of words in the first sentence of the passage. Record this number. Repeat this for 30 sentences. This your sample of size 30. Dotplot your data and describe the shape. Determine the sample median. Next obtain a 95% confidence interval for the true median sentence length. Locate the interval on your dotplot. What does it mean?

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2000-08-26