Statistics HW.
halajaName________________
HW 4 (Chapter 3)
Due 2/13/15
(a) Compute the sample mean and standard deviation. Minitab provides the following output;
Descriptive Statistics: C1
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
C1 54 0 57.41 1.61 11.81 35.00 48.00 56.50 64.25 85.00
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(b) Using 7 classes, Minitab draws this histogram. Verify the data is bell-shaped. Why is this an important part of using the empirical rule?
(d) Determine the percentage of all patients that have serum HDL within 3 standard deviations of the mean according to the Empirical Rule.
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(e) Determine the percentage of all patients that have serum HDL between 33.79 and 69.22 according to the Empirical Rule.
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(f) Determine the actual percentage of patients that have serum HDL between 33.79 and 69.22.
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2. A group of Brigham Young University-Idaho students (Matthew Herring, Nathan Spencer, Mark Walker, and Mark Steiner) collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted (construction) speed limit was 25 mph. The recorded speeds for 14 randomly selected vehicles are given below:
20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40
Minitab provides the following descriptive statistics;
Descriptive Statistics: C1 Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum C1 14 0 32.14 1.65 6.18 20.00 27.75 32.50 38.25 40.00 |
(a) Find the mean, median, and mode of this data.
(b) Describe what you would expect to happen to the mean and median if someone sped through the construction zone at 100 mph. (Use the word resistant correctly in your explanation).
(c) Find the sample standard deviation and variance for this data. Give a short explanation of what it would mean if a data set were to have a very, very small standard deviation.
(d) Would it be appropriate to use Chebyshev’s Inequality with this data? Why?
(e) Give the five-number summary, find the IQR, check for outliers, and draw a boxplot for this data
(f) Based on the information above, describe the shape of this distribution. Based on the shape of the distribution, what would be the measure of central tendency (mean or median) and measure of dispersion (standard deviation or interquartile range) to report?
3. NBA superstar Michael Jordan is 78 in. tall and WNBA basketball player Rebecca Lobo is 76 in. tall. Jordan is obviously taller by 2 in., but which player is relatively taller? Does Jordan’s height among men exceed Lobo’s height among women? Men have heights with a mean of 69.0 in. and a standard deviation of 2.8 in.; women have heights with a mean of 63.6 in. and a standard deviation of 2.5 in. (based on data from the National Health Survey). Use z-scores to determine which player is relatively taller.
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