CSL 4B Activity

  1. Login, open Minitab, and open ‘Physical Measurements Worksheet’. Review variables on sheet entitled ‘Physical Measurements Data Set’. Use the Minitab Worksheet contained on the disk given out to you.
  2. In today’s CSL you will be working with numerical (quantitative) variables. You will be practicing/applying what you studied in A-6 of Cyberstats and Chapter 2 of Heckard/Utts. Today’s work focuses on heights and weights of males and females and what they regard as their ideal heights and ideal weights (or what they wished they were). We all know that males are, on the average, taller and heavier than females. How much heavier? How much taller? Do males wish they were taller? How about females? We suspect (know?) that females wish they weighed less—how much? How about males: do they also wish, on the average, that they weighed less? Or more? The variables we will work with are in

Col. 4: Height of students;
Col. 41: Weight of students
Col. 43: Difference between a males actual height and his ‘ideal height’
Col. 44: Difference between a females actual height and her ‘ideal height’
Col. 50: Difference between the actual weight of a male and his desired weight
Col. 51: Difference between the actual weight of a female and her desired weight

Heights:

  1. Obtain the numerical descriptive for the heights of male and female students (click Stat, Basic statistics, Display descriptive statistics, variable ‘height’ in C4, by variable and choose ‘gender’ in C2). You will obtain lots of numerical statistics for both males and females. From the output, answer the following questions:

i. What is the average weight of males? ______ Of females? ______

ii. What is the standard deviation of male heights? _____ Of females? _____

iii.  Give the 5-number summary of male weights and female heights: 

      Males:     min          Q1          median        Q3             max

                    ____         ____      _____         _____         _____

      Females:     min         Q1         median         Q3         max

                       ____       ____        ____         ____       ____

      iv.  If we use the mean, how much taller are males than females, on the average? ___ 

      v.  If we use the median, how much taller are males than females, on the average? ___

      vi.  What is the interquartile range for males? _______ For females? ______

      vii.  What is the height such that 25% of male heights are less than it? ______ 

      viii.  What is the height such that 25% of female heights are greater than it? ______

      ix.  A mild outlier is a value that is more than 1.5 IQR’s below the 1st quartile or 1.5 IQR’s above the 3rd quartile. An extreme outlier is a value more than 3 IQR’s below the 1st quartile or more than 3 IQR’s above the 3rd quartile. Determine what the cutoff values are for mild outliers and extreme outliers for both males and females. 

                                    Male cutoffs         Female cutoffs

      Mild Outliers: < _____or > ______ < _____or > ______

      Extreme Outliers: < _____or > ______ < _____or > ______

       

    b.  Now obtain graphical displays of the heights of males and females.
    1. Obtain a histogram of the heights of both males and females. (click Graph, character graphs, histograms. For variables select height and click on by variable gender, then OK.
    2. Describe the shape (symmetric or skewed) of heights of males and females.

      Males: __________ Females: __________

       

    1. Obtain a boxplot of male and female heights. (follow the same procedure as for histograms). The box covers the middle 50% of the data. Is the box for males mostly to the right of the box for females? Or don’t they overlap? ___________
    c.  Switch attention now to the difference between actual heights and ‘wished for’ heights. This difference
        (actual height - wished for height) is stored in Col. 43 for males and Col. 44 for females.
    1. Obtain a histogram of the difference in actual and wished for heights for females and describe its shape: symmetric or skewed? _______
    2. Obtain a histogram of the difference in actual and wished for heights for males and describe its shape: symmetric or skewed? _______. Comment: Look at the interval with midpoint ‘0’. If this were removed, how would you describe the shape? Symmetric or skewed? ________. What does this interval say about what males desire for their ideal height?

      3. ---------------------------------------------------------------------------------------------------

    3. Obtain numerical descriptive statistics for the differences in heights for both males and female.

      4. Describe the average change in heights for males ________ and females _______.

      Do they seem to be about the same? Or different? __________ What is the difference between the desired difference for males vs desired difference for females in ? _______

    4. Test the hypothesis that the difference in actual and ideal heights for males is 0 vs the hypothesis that the difference is positive. Do this a also for females.(click statistics, basic statistics, 1-sample t, choose for the variables Col. Col. 43 and Col. 44, and do a one-sided alternative (greater than)).

                    H0 : m = 0 vs H1 m > 0 P-value = _____. Decision: Reject H0 ? No ___ Yes ____

            v. Obtain 95% confidence intervals for the differences for both males and females.

Confidence interval for difference in height: Males: _________________
Females: _________________

Obtain 99% confidence intervals for the differences for both males and females.

Confidence interval for difference in height: Males: _________________

Females: _________________

Name _________________________ Section: ______ Id# ____________

Name _________________________ Section: ______ Id# ____________

Name _________________________ Section: ______ Id# ____________

Name _________________________ Section: ______ Id# ____________

Name _________________________ Section: ______ Id# ____________

Name _________________________ Section: ______ Id# ____________