BACKGROUND: Your friend Sarah was at the warehouse store and saw two 8-packs of toothbrushes, one from a generic brand,

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BACKGROUND: Your friend Sarah was at the warehouse store and saw
two 8-packs of toothbrushes, one from a generic brand, Brand-A, and
another from a name-brand, Brand-B. The Brand-A toothbrushes seemed
to be very similar to the Brand-B toothbrushes, and yet were almost
half the price. Sarah has had experience with the Brand-B
toothbrushes and feel they are an acceptable product, but she was
concerned about the service life of the Brand-A toothbrushes. That
is, Sarah was concerned that the Brand-A toothbrushes wouldn’t last
as long as the Brand-B toothbrushes. Being both an inquisitive and
a patient person, Sarah decided to purchase both 8-packs of
toothbrushes and record the number of days that she could use each
toothbrush, even if it took years to conduct this experiment. At
the end of the experiment, Sarah collected the following data.
Unless stated otherwise, assume for the purposes of this
assignment, that the following samples are random and
independent.
• Service life of the Brand-A toothbrushes, in days: 32, 34, 32,
38, 35, 32, 35, 36 • Service life of the Brand-B toothbrushes, in
days: 36, 38, 42, 35, 38, 38, 40, 37
Sarah realizes that you are taking a Statistics course, and asks
for your help in determining whether or not the Brand-B
toothbrushes have a significantly longer service life than the
Brand-A toothbrushes. To prepare for much of the upcoming final
exam, you realize that you can use her data to practice some of the
topics that you have learned in the course up until this point. You
agree and decide to answer the following questions. You also decide
it is best to follow these instructions from the Instructor’s
Policy of the course syllabus:
indicate the units of measurement for final solutions, where
applicable, and
roundfinalnumericalsolutionstothefourthdecimalplace,thoughtrailingzerosdonotneed
to be stated.
1. (0 points: no work/solution needed) To confirm that you have
loaded the correct data into StatCrunch, or another statistical
software package or calculator, please check that the sample mean
for the Brand-A service life data set is x ̄A = 34.25 days and the
sample mean for the Brand- B service life data set is x ̄B = 38
days.
2. (10 points: you must do your own work!) Determine the median
for the Brand-A service life data set, and the median for the
Brand-B service life data set.