LOS H requires us to:
distinguish between a point estimate and a confidence interval estimate of a population parameter
a. The confidence interval is a range within which we can assert, with a probability of 1-α, the degree of confidence that the range will contain the parameter.
b. Thus, a 95% confidence interval would have two interpretations:
i. One, the probabilistic interpretation, that is, in repeated sampling, 95% of the confidence intervals will contain the parameter (like the population mean, µ).
ii. And two, the practical interpretation, that is, we have a 95% confidence that the parameters (like the population mean, µ) lies within the specified interval.
c. We can calculate the confidence intervals using the following formula:
Where,
i. Point estimate: A point estimate of the parameter (a value of a sample statistic), such as the sample mean.
ii. Reliability factor: A number based on the assumed distribution of the point estimate and the degree of confidence (1 − α) for the confidence interval.
iii. Standard error: The standard error of the sample statistic providing the point estimate.
d. More specifically, for the sample mean as the point estimate, we can calculate the confidence interval using the following equation: