Question

a physical trainer has four workouts that he recommends for his clients. the workouts have been designed so that the average maximum heart rate achieved is the same for each workout. to test this design he randomly selects twenty people and randomly assigns five of them to use each of the workouts. during each workout, he measures the maximum heart rate in beats per minute with the following results. can the physical trainer conclude that there is a difference among the average maximum heart rates which are achieved during the four workouts?

Answer 1

The P-value of 0.06 is greater than the significance level (0.05), hence we fail to reject the null hypothesis.

So, we cannot conclude that there is no difference between the average maximum heart rates that are achieved during the four workouts.

ANNOVA: Single factor

Groups       Count     Sum    Average       Variance

Workout 1        5         842      168.4             174.3

Workout 2       5         881        176.2             79.7

Workout 3       5         857        171.4              66.8

Workout 4       5          934        186.8            117.2

ANNOVA

Source of Variance  ss        df  MS       F                P-value         F-crit

Between groups      976.2   3  325.4   2.971689   0.063098    3.238872

Within groups           1752     16  109.5

Total                         2728.2   19

The null hypothesis is : u1=u2=u3=u4

Alternative hypothesis: At least one of the u is not  equal.

The significance level=0.05

Analyzing the sample data:

F statistics is given by:

$F=\frac{MSB}{MSE}$

= 2.97

F-critical $= 3.24$

The P-value = 0.06

Since, the P-value of 0.06 is greater than the significance level (0.05), hence we fail to reject the null hypothesis.

So, we cannot conclude that there is no difference between the average maximum heart rates that are achieved during the four workouts.

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