Question

Dan, a trainer at the Popular Gym, was interested in determining whether or not the members at the gym exercise, on average, more than 4 hours per week. Dan records the number of hours per week that 25 randomly selected members spend exercising and determines that the test statistic is t = 2.17. Which of the following is correct? .

The result is significant at the 0.05 level but not the 0.01 level.

B. The result is not significant at any reasonable level of significance.

C. The result is significant at the 0.01 level but not the 0.05 level.

D. There is insufficient evidence to conclude that the members, on average, spend more than 4 hours per week exercising

Answer 1

Given that, sample size (n) = 25

Null and alternative hypotheses are,

Test statistic is, t = 2.17

Degrees of freedom (DF) = n-1 =25 -1 = 24

t-critical value at significance level = 0.05 with DF = 24 is,

t* = 1.711

Here, test statistic = 2.17 > t* = 1.711

Implies that, we reject the null hypothesis.

Now, t-critical value at significance level = 0.01 with DF = 24 is, t* = 2.492

Here, test statistic = 2.27 < t* = 2.492

Implies that, we fail to reject the null hypothesis.

Hence, correct answer is, the result is significant at the 0.05 level but not the 0.01 level.