STAT 1000 - Unit 6 Exam Questions and Answers Graded A+
statistical inference - Answers - provides methods for drawing conclusions about a population from
sample data
how "good" of an estimator is Xbar? - Answers - the probability that Xbar = μ is equal to 0, because of
continuity (Xbar is a continuous variable)
- reporting the sample mean alone gives no information as to how accurate we believe our estimate to
be
- instead, we would like to use the sample mean to construct an interval of values to estimate the
population mean μ
95% confidence interval for μ - Answers (xbar - 1.96*σ/√n, xbar + 1.96*σ/√n)
we interpret the 95% confidence interval for μ as follows: - Answers - if we repeatedly took simple
random samples of the same size from the same population and constructed the interval in a similar
manner, 95% of all such intervals would contain the true mean μ of the population
estimate - Answers - best guess at the true value of the parameter we're trying to estimate
margin of error - Answers - reflects how accurate we believe our estimate to be
confidence level, C - Answers - gives the probability that the interval will contain the true value of the
population mean μ
general level C confidence interval formula - Answers xbar ± z*σ/√n
- where z* is the value of Z such that P(-z* ≤ Z ≤ z*) = C
z* - Answers - the values of z* that mark off a specific area under the standard normal curve are called
critical values of the distribution
P(Z ≤ -z*) or P(Z ≥ z*) - Answers 1 - C/2
effect of confidence level on margin of error - Answers - when the confidence level increases, the margin
of error (and thus the length of the interval) also increases
- thus if we increase the confidence level, we must sacrifice our precision of estimation
- if we want to be more confident that our interval contains μ, then we have to expand the interval
sample size on margin of error - Answers - higher sample size results in a lower margin of error (and
hence a narrower confidence level)
- we see that taking a sample that is four times greater results in a margin of error that is only half as
large
statistical inference - Answers - provides methods for drawing conclusions about a population from
sample data
how "good" of an estimator is Xbar? - Answers - the probability that Xbar = μ is equal to 0, because of
continuity (Xbar is a continuous variable)
- reporting the sample mean alone gives no information as to how accurate we believe our estimate to
be
- instead, we would like to use the sample mean to construct an interval of values to estimate the
population mean μ
95% confidence interval for μ - Answers (xbar - 1.96*σ/√n, xbar + 1.96*σ/√n)
we interpret the 95% confidence interval for μ as follows: - Answers - if we repeatedly took simple
random samples of the same size from the same population and constructed the interval in a similar
manner, 95% of all such intervals would contain the true mean μ of the population
estimate - Answers - best guess at the true value of the parameter we're trying to estimate
margin of error - Answers - reflects how accurate we believe our estimate to be
confidence level, C - Answers - gives the probability that the interval will contain the true value of the
population mean μ
general level C confidence interval formula - Answers xbar ± z*σ/√n
- where z* is the value of Z such that P(-z* ≤ Z ≤ z*) = C
z* - Answers - the values of z* that mark off a specific area under the standard normal curve are called
critical values of the distribution
P(Z ≤ -z*) or P(Z ≥ z*) - Answers 1 - C/2
effect of confidence level on margin of error - Answers - when the confidence level increases, the margin
of error (and thus the length of the interval) also increases
- thus if we increase the confidence level, we must sacrifice our precision of estimation
- if we want to be more confident that our interval contains μ, then we have to expand the interval
sample size on margin of error - Answers - higher sample size results in a lower margin of error (and
hence a narrower confidence level)
- we see that taking a sample that is four times greater results in a margin of error that is only half as
large
