Chapter 11.2, Problem 38E

(a)

To determine

To summarize these data in a two-way table.

Explanation of Solution

In the question, it is given that aspirin prevents blood from clotting and so help prevent strokes. Thus, the data on the strokes for the two-year study is given in the question. Thus, the summary of these data in a two-way table can be represented by the number of no strokes is the number of patients decreased by the number of strokes, that is,

  

(b)

To determine

To make a graph to compare the success rates for the four treatments and describe what you see.

Explanation of Solution

In the question, it is given that aspirin prevents blood from clotting and so help prevent strokes. Thus, the data on the strokes for the two-year study is given in the question. Thus, the summary of these data in a two-way table can be represented by the number of no strokes is the number of patients decreased by the number of strokes, that is,

  

So therefore the proportion in each group is the number of strokes/ no strokes divided by the row total given in the last column is calculated as:

  

Thus, the graph to compare the success rates for the four treatments can be constructed as:

  

Thus, by looking at the histogram we note that the proportions of strokes/no strokes do not seems to vary much by group.

(c)

To determine

To explain in words what the null hypothesis $H_0:p_1=p_2=p_3=p_4$ says about subjects’ smoking habits.

Answer to Problem 38E

It says proportion of successes for each treatment is the same.

Explanation of Solution

In the question, it is given that aspirin prevents blood from clotting and so help prevent strokes. Thus, the data on the strokes for the two-year study is given in the question. Thus, the summary of these data in a two-way table can be represented by the number of no strokes is the number of patients decreased by the number of strokes, that is,

  

Thus, it is given the null hypothesis in the question as:

  $H_0:p_1=p_2=p_3=p_4$

And the null hypothesis says about the subjects’ smoking habits that this means that the proportion of successes for each treatment is the same.

(d)

To determine

To find the expected counts if null hypothesis is true and display them in a two-way table of observed counts.

Explanation of Solution

In the question, it is given that aspirin prevents blood from clotting and so help prevent strokes. Thus, the data on the strokes for the two-year study is given in the question. Thus, the summary of these data in a two-way table can be represented by the number of no strokes is the number of patients decreased by the number of strokes, that is,

  

Thus, it is given the null hypothesis in the question as:

  $H_0:p_1=p_2=p_3=p_4$

Thus, the expected counts are the row total multiplied by the column total, divided by the sample size $n=6602$ as: