Variable N Mean StDev SE Mean 95% CI
Sleep 20 6.950 1.572 0.352 (6.214, 7.686)
Give me the interpre the 95% confidence interval fir the hours of sleep a student gets.
If this is for one student:
95% = mean ± 1.96 SD = 6.95 ± 1.96 (1.572) = ?
If it is for the mean of students:
95% = mean ± 1.96 SEm = 6.95 ± 1.96 (.352) = ?
The 95% confidence interval for the hours of sleep a student gets is (6.214, 7.686).
To obtain this confidence interval, a sample of students' sleep data was collected. The variable "Sleep" represents the number of hours of sleep for each student. The sample size (N) is 20, and the mean (Mean) is calculated to be 6.950 hours with a standard deviation (StDev) of 1.572 hours.
The standard error of the mean (SE Mean) is calculated by dividing the standard deviation by the square root of the sample size. In this case, the SE Mean is 0.352.
To construct the confidence interval, we use the formula:
CI = Mean ± (Z * SE Mean)
In this formula, Z is the critical value that corresponds to the desired confidence level. For a 95% confidence level, the critical value is approximately 1.96.
Plugging in the values, we can calculate the lower and upper bounds of the confidence interval:
Lower bound = Mean - (Z * SE Mean)
Upper bound = Mean + (Z * SE Mean)
Lower bound = 6.950 - (1.96 * 0.352) = 6.214
Upper bound = 6.950 + (1.96 * 0.352) = 7.686
Therefore, the 95% confidence interval for the hours of sleep a student gets is (6.214, 7.686). This means that we can be 95% confident that the true population mean falls within this range.