CSL 5A Activity
(Continuation of CSL 4B)
  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 weights of males and females and what they regard as their ideal weights (or what they wished they were). We all know that males are, on the average, heavier than females. How much heavier? 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? And how do males and females view their weight, in terms of their actual weight? If time permits, some other comparisons of means will be made. The variables we will work with are in
Weights
  1. Obtain the numerical descriptive statistics for the weights of male and female students (click Stat, Basic statistics, Display descriptive statistics, variable 'weight' in C6, 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:

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

    2. What is the standard deviation of male weights? _____       Of female weights? _____

    3. If we use the mean, how much more do males weigh than females, on the average? ______

  2. Switch attention now to the difference between actual weights and 'wished for' weights. This difference (actual weight - ideal weight) is stored in Col. 50 for males and Col. 51 for females.


    1. Obtain a histogram of the difference in actual and wished for weights for females and describe its shape: symmetric or skewed? _______

    2. Obtain a histogram of the difference in actual and ideal weights for males and describe its shape: symmetric or skewed? _______.

    3. Obtain numerical descriptive statistics for the differences in weights (actual - ideal) for both males and female.

      What is the average difference between actual and ideal weights for males ________ and females _______.

      Do they seem to be about the same? Or different? ________

    4. Test the hypothesis that the difference in actual and ideal weights for males is 0 vs the hypothesis that the difference is positive. Do this also for females.(click statistics, basic statistics, 1-sample t, choose for the variables Col. 50 and Col. 51, and do a one-sided alternative (greater than)). Let mFD denote the (population) mean difference in actual vs ideal weights for females and mMD denote the (population) mean difference in actual vs ideal weights for males.

    5. Specify the null and alternative hypothesis for testing the hypothesis about the difference in actual and ideal weights for males and do also for females.

      Males: H0 : _____      H1 : _____       Females: : H0 : _____       H1 : ______      

    6. In terms of the average difference in weights, when should the null hypotheses be rejected?

      Answer: ______________________________________________________

    7. P-value for 'Males' _____.       Decision: Reject H0 ? No ___ Yes ____
      P-value for 'Females' _____.       Decision: Reject H0 ? No ___ Yes ____

    8. Obtain 95% confidence intervals for the differences for females.

      Confidence interval for difference in weight: Females: _________________

      Obtain 99% confidence intervals for the differences for females.

      Confidence interval for difference in weight: Females: _________________

    9. Which the two confidence intervals is longer? 95% _____ or 99% ______?

    10. Suppose we wanted to know whether or not the difference in actual and ideal weights is the same for males and females. We would perform a two-sample test of the hypothesis H0 : mFD = mMD vs H1 : mFD ¹ mMD . Do this test-when should H0 be rejected? (Use two-sample t-test).
      Reject? No ___ Yes ___.       P-value of test is ________.

  3. Suppose we wanted to test whether or not three or more population means are equal or not. For example, one would naturally expect that one's view of their weight (overweight, about right, underweight) would depend strongly on how much one actually weights. In this case, there are three population means we are concerned about: mover , mright , and munder .


    1. Right the appropriate null and alternative hypotheses for comparing these three means.

      H0 : ___________________       H1 : _____________________

    2. Obtain the sample means and sample standard deviations for the weights by view of weight (click stat, basic statistics, display descriptive statistics. Choose as the variable weight, and select view of weight as the by variable).
      View of weight average standard deviation 
      	Over		_______		_______

	About right 	_______		_______

	Under		_______		_______

      Do the averages seem to be about the same? Or quite a bit different? __________

    3. The SD for 'Overweight' is larger than the SD's for the other two groups-what does this say about the weights in the overweight' group vs the weights in the other two groups?

    4. Test the hypothesis. (click stat, ANOVA, One-way. Choose 'weight' as the response and 'view of weight' as the factor (comparison group). and OK. You will see a One Factor Analysis of Variance come up and within this a name labeled 'F' and p (for p-value -this p-value is what you use to do the test.)

      Should H0 be rejected? Yes ___ No ___.

  4. Do average GPA's vary in terms of how one view's their weight? Test the hypothesis that the average GPA's are the same in the three groups of how people view their weight. Which of the three groups has the highest aver GPA? How do the other two groups compare? Continued on next page


    1. Reject the null hypothesis? Yes ____       No ____

    2. Group with the highest average GPA: __________

    3. Comparison of other two groups: _____________________________________

  5. Just for curiosity's or for the sake of fun! One of the variables on the Physical Measurements data worksheet asks: 'How many days per month (usually) do you drink at least two beers?' How do the Asians, African Americans/Blacks, Caucasians, and All Others compare on this? Do a one-factor analysis of variance with '2Beers' as the response and 'Race' as the factor. Is there a significant difference between the races on this variable?


    1. Who drinks 2beers the most days in a month? Who drinks at least 2beers the least number of times?

    2. Are the averages statistically significantly different? Yes ___       No ___

    3. Obtain histograms of the variable '2beers' by race. Do the histograms appear to be symmetric?
      Yes ___       No ___

Name : ___________________________      Section: ____________       ID# _________

Name : ___________________________      Section: ____________      ID# _________

Name : ___________________________      Section: ____________      ID# _________

Name : ___________________________      Section: ____________      ID# _________

Name : ___________________________       Section: ____________       ID# _________