Question

define each of the following
(a) point estimate
(b) confidence interval
(c) level of confidence
(d) margin of error
(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
(d) define margin of error. choose the correct answer
a. a numerical distance equal to the width of a confidence interval
b. the expected proportion of confidence intervals that will not contain the parameter if a large number of different samples is obtained
c. the center of a confidence interval, a confidence interval can be written as margin of error ± point estimate
d. a numerical distance that determines the width of a confidence interval, a confidence interval can be written as point estimate ± margin of error

Explanation:

• For (c), the level of confidence is about the proportion of confidence intervals (from many samples) that contain the parameter. Option A correctly describes this as it refers to the expected proportion of confidence intervals (from different samples) containing the parameter. Option B is about individual values in a confidence interval (wrong focus). Option C and D refer to a single confidence interval's probability (incorrect as level of confidence is about multiple intervals from repeated sampling).
• For (d), the margin of error is a numerical value. A confidence interval is written as point estimate ± margin of error. Option D correctly states that it is a numerical distance determining the width (since width = 2×margin of error) and the correct formula for confidence interval. Option A is wrong as width = 2×margin of error (not equal). Option B is about non - containing intervals (not margin of error definition). Option C has the formula reversed (should be point estimate ± margin of error).

Answer:

(c) A. The expected proportion of confidence intervals that will contain the parameter if a large number of different samples is obtained
(d) D. A numerical distance that determines the width of a confidence interval; a confidence interval can be written as point estimate ± margin of error