Question

define each of the following
(a) point estimate
(b) confidence interval
(c) level of confidence
(d) margin of error
(b) define confidence interval. choose the correct answer
a. an interval of numbers that defines the range of the middle specified percentage of all sample data
b. an interval of numbers for a quantitative variable within which a specified percentage of all known values of the variable fall
c. an interval of numbers for a sample statistic given a population
d. an interval of numbers for an unknown parameter based on a point estimate
(c) define level of confidence. choose the correct answer
a. the expected proportion of confidence intervals that will contain the parameter if a large number of different samples is obtained
b. the expected proportion of the individual values of a quantitative variable that will be contained by a confidence interval
c. the probability that a confidence interval contains the parameter
d. the probability that a confidence interval contains an individual value of a quantitative variable

Explanation:

• Confidence Interval: A confidence interval is an interval of numbers for an unknown parameter based on a point estimate. It gives a range within which the true population parameter is likely to lie.
• Level of Confidence: The level of confidence is the expected proportion of confidence intervals that will contain the parameter if a large number of different samples is obtained. It represents the long - run frequency of intervals that capture the true parameter.

Answer:

• (b) D. An interval of numbers for an unknown parameter based on a point estimate
• (c) A. The expected proportion of confidence intervals that will contain the parameter if a large number of different samples is obtained