Lecture 14. Chapter 7 Statistical Intervals Based on a Single Sample. What is a confidence interval (CI)?
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Statistical Intervals Based on a Single Sample
The point estimate provides only a single value estimate for a population parameter. It does not provide any information on how “good” the estimate is, or how close it is to the real value of the parameter.
A confidence interval provides an interval along with a certain confidence probability value (1) for a population parameter. A CI indicates the percentage of the CIs formed from a number of different samples of same size that would contain the real value of the estimated population parameter.
Let the the 95% confidence interval for the mean product length, calculated using a certain sample, is [24,29]. This means that if we kept taking similar samples to which we calculated the above CI from, about 95% of the CIs that we form will contain the real value of the mean length. Also, since (1) = 0.95, = 0.05
WHEN THE VARIANCE IS KNOWN
WHEN THE VARIANCE IS UNKNOWN
follows a t (Student’s t) distribution with (n-1) degrees of freedom (df). The df is denoted by .