Question

define each of the following
(a) point estimate
(b) confidence interval
(c) level of confidence
(d) margin of error
(a) define point estimate. choose the correct answer.
oa. the expected value of a dependent variable based on the value of an independent variable
ob. the value of a statistic that estimates the value of a parameter
oc. the value of a parameter at a specified time
od. the result of one trial in an experiment
(b) define confidence interval. choose the correct answer.
oa. an interval of numbers that defines the range of the middle specified percentage of all sample data
ob. an interval of numbers for a quantitative variable within which a specified percentage of all known values of the variable fall
oc. an interval of numbers for a sample statistic given a population
od. an interval of numbers for an unknown parameter based on a point estimate

Explanation:

• (a) Point estimate: A point estimate is a single value (a statistic) used to estimate an unknown population parameter. For example, the sample mean \(\bar{x}\) is a point estimate of the population mean \(\mu\).
• (b) Confidence interval: A confidence interval is an interval of values constructed from sample data so that the population parameter is likely to occur within that interval at a specified confidence level. It is based on a point estimate and provides a range of plausible values for the unknown parameter.

Answer:

• (a) C. The value of a statistic that estimates the value of a parameter
• (b) D. An interval of numbers for an unknown parameter based on a point estimate