Question

Sophia, a yoga instructor at Yoga for You, selected random samples of 210 students from a nearby high school and 210 students from a nearby college to compare levels of physical fitness. The mean and standard deviation of the fitness levels of the high school students were 82 and 14 respectively. The mean and standard deviation of the fitness levels of the college students were 86 and 17 respectively. She conducted a two-sided t-test with a resulting t-value of 2. 63. Lf a = 0. 05, what is an appropriate conclusion from this study?

Because the sample means only differ by four, the population means are not significantly different.


Because the second group has a larger standard deviation, their mean fitness score is significantly higher.


Because the second group has a larger standard deviation, the mean fitness score of the first group is significantly higher


Because the p-value is greater than a 0. 05, the mean fitness scores for the two groups of students are not significantly different.


Because the p-value is less than a 0. 05, the mean fitness scores for the two groups of students are significantly different

Answer 1

Answer: Choice D

Because the p-value is less than 0.05, the mean fitness scores for the two groups of students are significantly different

========================================================

Step-by-step explanation:

Use a T calculator to find that P(T > 2.63) = 0.00459 approximately when we have 209 degrees of freedom.

Double this to get 2*0.00459 = 0.00918 and this is the approximate p-value

Since the p-value is less than alpha = 0.05, this means we reject the null and conclude that the two population means are significantly different.