Dan, a trainer at the Popular Gym, was interested in comparing levels of physica

Question

Dan, a trainer at the Popular Gym, was interested in comparing levels of physical fitness of students attending a nearby community college and those attending a 4-year college in town. He selected a random sample of 320 students from the community college. The mean and standard deviation of their fitness scores were 95 and 10, respectively. Dan also selected a random sample of 320 students from a 4-year college. The mean and standard deviation of their fitness scores were 92 and 13, respectively. He then conducted a two-sided t-test that resulted in a t-value of 3.27. Which of the following is an appropriate conclusion from this study?

(A) Because the sample means only differed by 3, the population means are not significantly different.

(B) Because the second group had a larger standard deviation, their mean fitness score is significantly higher.

(C) Because the second group had a larger standard deviation, the mean fitness score of the first group is significantly higher.

(D) Because the p-value is less than a = 0.05, the mean fitness scores for the two groups of students are significantly different.

(E) Because the p-value is greater than a = 0.05, the mean fitness scores for the two groups of students are significantly different.

Explanation / Answer

This is a two-tailed t test.

Here,

n1 = 320
n2 = 320

So

df = n1 + n2 - 2 = 638

Hence, the P value here is

Pvalue = 0.001133334

[critical value is tcrit = +/- 1.964]

As this is a small P value, P < 0.05, then the difference is statistically significant.

Hence,

OPTION D: (D) Because the p-value is less than a = 0.05, the mean fitness scores for the two groups of students are significantly different. [ANSWER, D]

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