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1.
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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.
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2.
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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.
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3.
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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.
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4.
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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
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5.
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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
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6.
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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?
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7.
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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?
