Standard error

Standard error is a number used when creating confidence intervals. Standard error is calculated by dividing the standard deviation of the sample by the square root of sample size n.

Example

Here's a sample question. Standard error will be in bold.

“

A random sample of Alzheimer's patients are tested to assess the amount of time in stage IV sleep. It has been hypothesized that individuals sufferering from Alzheimer's Disease may spend less time per night in the deeper stages of sleep. Number of minutes spent is Stage IV sleep is recorded for sixty-one patients. The sample produced a mean of 48 minutes with a standard deviation of 14 minutes of stage IV sleep over a 24 hour period of time. Compute a 95 percent confidence interval for this data. What does this information tell you about a particular individual's (an Alzheimer's patient) stage IV sleep?

”

Parametres:

μ = 48

σ = 14

n = 61

Conditions:

SRS? Yes, given.

Normal? Large sample size. Yes.

Independent? N>= 10n? Yes.

Calculation:

μ +- T*(σ/sqrt(n))

48 +- 2(14/sqrt(61))

48 +- 2(14/7.8102)

48 +- 3.58503 = (44.414, 51.58)