Chapter 4, Problem AP1.15CPT

(a)

To determine

To write few sentences comparing the distribution of cardiovascular fitness gains from the two elliptical machines.

Explanation of Solution

Shape: we note that the distribution of machine A is roughly symmetric because most of the data values lies roughly in the middle of the stem and leaf diagram. The distribution of machine B appears to be skewed to the left because most of the data values lies near the bottom of the stem and leaf diagram.

Centre: the centre of the machine B appears to be slightly higher than the centre for machine A because most of the data values of machine A are cantered at stem two while most of the data values are cantered at stem three in the diagram.

Spread: The spread of machine B is higher than the spread for Machine A because Machine A uses only four stems while Machine B uses six stems in the diagram.

Unusual features: There appear to be no outliers because there are no gaps in either stem and leaf diagram.

(b)

To determine

To identify which machine should be chosen if the company wants to advertise it as achieving the highest overall gain in cardiovascular fitness and explain.

Answer to Problem AP1.15CPT

Machine B.

Explanation of Solution

Machine B should be chosen if the company wants to advertise it as achieving the highest overall gain in cardiovascular fitness because the highest value comes from this data set, which, when advertising, is the set that is to be used.

(c)

To determine

To identify which machine should be chosen if the company wants to advertise it as achieving the most consistent gain in cardiovascular fitness and explain.

Answer to Problem AP1.15CPT

Machine A.

Explanation of Solution

Machine A should be chosen if the company wants to advertise it as achieving the most consistent gain in cardiovascular fitness because the most consistent gain is for the machine with the smallest spread.Machine A has a smaller spread, because it does not have any values in the first row ( $5$ ) and in the last row ( $0$ ), while machine B does have values in these rows.

(d)

To determine

To give one reason why the advertising claims of the company for this experiment would be limited and explain how the company could broaden that scope of inference.

Explanation of Solution

Volunteers were used for this experiment and these volunteers may be different in some way from the general population of those who are interested in cardiovascular fitness. Another reason is that the experiment was conducted at only one fitness centre. Results may vary at other fitness centres in this city and in other cities.