Final answer:
The number of participants included in the one-sample t test analysis is 144, calculated using the formula n = (s / SE)², with a standard deviation of 84 and a standard error of 7.
Step-by-step explanation:
The student's question is about calculating the number of participants included in a one-sample t test analysis given the sample mean, the standard error, and the standard deviation. To find the sample size, we use the relationship between the standard error of the mean, the standard deviation, and the sample size (n). The standard error (SE) is calculated using the formula SE = s / √n, where 's' is the standard deviation, and 'n' is the sample size.
Given that:
- Sample mean = 283 (this is not used in the calculation but given for context)
- Standard error (SE) = 7
- Standard deviation (s) = 84
By rearranging the formula SE = s / √n to solve for n, we get:
n = (s / SE)²
Now we plug in the given values:
n = (84 / 7)²
n = (12)²
n = 144
Therefore, the number of participants included in the analysis is 144.