Question

Resting pulse rate is an important measure of the fitness of a person's cardiovascular system with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled in the School of Agriculture was selected and the mean pulse resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population.

A possible Type II error would be to:
Conclude that the students are less fit (on average) than the general population when in fact they have equal fitness on average.
Conclude that the students have the same fitness (on average) as the general population when in fact they are less fit on average.
Conclude that the students have the same fitness (on average) as the general population when in fact they are the same fitness level on average.
Conclude that the students are less fit (on average) than the general population, when, in fact, they are less fit on average.
Conclude that the students have the same fitness (on average) when in fact they are more fit on average.

Answer 1

A Type II error in this context would mean incorrectly concluding that the fitness of the School of Agriculture male students matches the general population's average when they are less fit.

Step-by-step explanation:

A Type II error in a hypothesis test occurs when we fail to reject the null hypothesis when it is false. When assessing the fitness of the School of Agriculture male students compared to the general population's mean pulse rate, a Type II error would occur if we conclude that the students have the same fitness (on average) as the general population when in fact they are less fit on average. This mistake means that we would wrongly retain our assumption (null hypothesis) that the agricultural students' mean resting pulse rate is not significantly higher than the general population's, even though the true state of nature is that the agricultural students are less fit with a higher resting pulse rate.

Answer 2

A Type II error in this statistical test would have the experimenter incorrectly failing to reject the null hypothesis, mistakenly concluding the students' fitness is equal to the general population when they are actually less fit.

Step-by-step explanation:

The concept in question relates to a statistical hypothesis test and specifically the idea of Type I and Type II errors. In hypothesis testing, a Type II error occurs when the null hypothesis is not rejected, even though the alternative hypothesis is true. In the context of this problem, the null hypothesis is that the mean resting pulse rate for the students is equal to the general population of adult males, which is approximately 72 bpm. A Type II error would therefore involve failing to reject the null hypothesis when in fact the students are less fit, meaning their true mean resting pulse rate is higher than the population average.

The correct answer to the question posed by the student, about a possible Type II error, would be: "Conclude that the students have the same fitness (on average) as the general population when in fact they are less fit on average." This is because the action described (not concluding the students are less fit when they actually are) directly corresponds to the definition of a Type II error.