Instructions: Answer each question, and when required explain your answer. Your explanation must be clear and complete. You may refer to your book, your notes and your homework papers.
  1. (Be prepared to make other kinds of charts too.)
  2. (Be prepared to discuss the advantages of other kinds of charts.) A survey of college students found that 67% have an after school job, 45% live off campus, 43% ride a bicycle to class, and 25% have not declared a major. Which would be the best choice to display this data: a bar chart, a line graph, a pie chart or a histogram? Justify your answer as to which is best (and why each of the others are not).
    Answer: These categories overlap, as is made clear by the fact that the percentages add to well over 100%; someone might well have both a job and live off campus. Thus it makes no sense to use pie charts, since the data do not represent parts of a whole. Nor is there any trend; the data may give a profile of the students but it does not involve numbers changing over time, so line graphs are not called for. Histograms are for when you have a list of data values, and you want to show how often the values fall in various ranges. Since we do not just have a list of numbers, we would not use a histogram. Thus the bar chart is best, since it can show our data, while none of the other options is appropriate.
  3. Do Problem 4 on page 545.
    Answer:
  4. Explain how to select a simple random sample of 7 elements from the whole numbers running from 1 to 100, using the table on page 570. What sample do you get? Explain in enough detail that I can verify that your sample is the one you should have gotten.
    Answer: Randomly pick a starting entry in the table, say the entry in row 5 column 3. Then read down and pick the last two digits of each entry, skipping an entry if it gives a number already chosen. (If the two digits are 00 then that counts as 100.) Here is the simple random sample I get: 26, 6, 59, 32, 25, 10, 20.
  5. Explain how to select a 40% independent sample from the whole numbers running from 1 to 10, using the table on page 570. What sample do you get? Explain in enough detail that I can verify that your sample is the one you should have gotten.
    Answer: Randomly pick a starting entry in the table, say the entry in row 2 column 4 (which is 64569). Then read down that column, counting from 1 to 10 as you go. Every time the last two digits of the entry gives a number between 1 and 40 inclusive, the number you counted is selected. The results are given in the following table, where the first column gives the count from 1 to 10, the second column gives the corresponding table entry, the third column gives its last two digits and the fourth column indicates whether we select the number in the first column or not:
     1     64569   69   do not select 1
     2     17707   07   do select 2
     3     60638   38   do select 3
     4     93608   08   do select 4
     5     78545   45   do not select 5
     6     39445   45   do not select 6
     7     50784   84   do not select 7
     8     33358   58   do not select 8
     9     36246   46   do not select 9
    10     17068   68   do not select 10
    
    Our 40% independent sample is thus {2, 3, 4}.
  6. Do Problem 37 on page 592.
    Answer: The book gives a solution on page 920.
  7. Consider the data 1, 5, 6, 6, 7, 8, 8, 9, 11, 20.