Question

For a one-sample t test if the sample standard deviation is 18 and the standard error of the mean is 3, how many participants were used in this study?

a. 4 participants
b. 36 participants
c. 144 participants
d. 324 participants

Answer 1

The number of participants used in the study with a sample standard deviation of 18 and a standard error of the mean of 3 is 36, which is option b.

Step-by-step explanation:

The student has asked how many participants were used in the study if the sample standard deviation is 18 and the standard error of the mean is 3. To answer this question, we utilize the formula for the standard error of the mean (SEM), which is SEM = s/√n, where 's' is the sample standard deviation and 'n' is the sample size.

Given that SEM is 3 and s is 18, we can solve for 'n' like so: 3 = 18/√n. By squaring both sides, we get 9 = 324/n, and then multiplying both sides by 'n' to isolate it on one side, we get 9n = 324. Finally, by dividing both sides by 9, we find that n = 36.

The sample size in this study was therefore 36 participants, which corresponds to option b. This is the correct answer.