Two animals C and B were tested according to the time to run a particular track with the following results:
Animal C
28
29
30
33
32
34
Animal B
27
32
33
30
30
28
Test whether the two animals have the same running capacity. The average
time for animal C is 31 and the average time for animal B is 30. The null hypothesis is that the two animals have the same running capacity, while the alternative hypothesis is that they have different running capacities.
To test this, we can use a two-sample t-test. The t-test statistic is calculated by subtracting the average time of animal B from the average time of animal C and then dividing by the standard error of the difference between the two sample means.
The t-test statistic for this data is:
t = (31 - 30) / sqrt((3.67^2)/6 + (3.16^2)/6) = 0.34 / 1.84 = 0.185
With 5 degrees of freedom (n1 + n2 - 2), and an alpha level of 0.05 (assuming a 95% confidence level), the critical t-value is approximately 2.571.
Since the calculated t-value of 0.185 is less than the critical t-value of 2.571, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that the two animals have different running capacities.