unit7 confidence intervals

Question 1

In statistical inference, we often construct confidence intervals for statistics.

Answer 1

False. We construct

confidence intervals for parameters, and never for statistics

Question 2

A confidence interval is a range of plausible values for a parameter

Answer 2

true

Question 3

The confidence level of an interval is determined by sample data.

Answer 3

false

We choose the confidence level

Question 4

The point estimate of µ lies at the midpoint of the confidence interval for µ.

Answer 4

True.
The point
estimate of µ is the value of X¯, which always falls at the midpoint of the interval.

Question 5

The confidence interval procedures of this section assume a normally distributed population,
but this assumption becomes less important as the sample size increases.

Answer 5

True. (Because of the

central limit theorem.)

Question 6

All else being equal, what is the effect of the following on the margin of error of a confidence interval
for µ?
(a) An increase in the sample size.
(b) An increase in the variance.
(c) An increase in the sample mean.
(d) An increase in the confidence level

Answer 6

everything but c

* an increase in confidence level inc Zalpha/2 which inc margin or error

Question 7

The variance of the t distribution is greater than the variance of the standard normal distribution.

Answer 7

true

Question 8

The mean of the t distribution is equal to the mean of the standard normal distribution

Answer 8

true

Question 9

As the degrees of freedom increase, the t distribution tends toward the standard normal distribution.

Answer 9

true

Question 10

The t distribution is equivalent to the standard normal distribution if the degrees of freedom are at least 30

Answer 10

False. Although the t distribution tends toward the standard normal distribution
as the degrees of freedom increase, there are still meaningful differences at 30 degrees of freedom
and above.

Question 11

Suppose that we should be using tα/2 in the formula to find a confidence interval for µ, but we mistakenly use zα/2 in its place. Would the interval found using zα/2 be wider or narrower than if we had used the appropriate tα/2 value?

Answer 11

The interval found using zα/2 would be narrower. Although narrower intervals are preferred, had
we made this mistake we would be reporting incorrect results. (But if the sample size is large the
mistake would have only a very small effect.)

Question 12

What types of violation of the normality assumption are very problematic for the t procedure? What types of violation of the normality assumption are not a big problem?

Answer 12

skewness and outliers =biggest problems for the t procedure (especially if the sample size is small).
If a distribution is roughly symmetric this type of violation of the normality assumption is not a big problem
any violations are less problem as sample size increases.

Question 13

The standard error of a statistic decreases as the sample size decreases.

Answer 13

False. The standard

error increases as the sample size decreases.

Question 14

The one-sample t procedures are robust to violations of the normality assumption.

Answer 14

True.

The t procedures work quite well in a variety of non-normal situations.

Question 15

The t procedures do not perform well when there is strong skewness or outliers in the data, especially for small sample sizes

Answer 15

true

Question 16

The width of a confidence interval for µ decreases as the sample size decreases

Answer 16

The width of a confidence interval increases as the sample size decreases.

Question 17

The width of a confidence interval for µ decreases as the variance increases

Answer 17

False. The width of a confidence interval increases as the variance increases.

Question 18

In practical problems, σ is usually known and thus we usually use z procedures instead of t procedures.

Answer 18

The vast majority of the time σ is an unknown quantity

Question 19

Standard errors are the estimated standard deviations of parameters in repeated sampling

Answer 19

False. A standard error is the estimated standard deviation of a statistic in repeated sampling.

Question 20

If the assumptions of a procedure used to calculate a 90% confidence interval are violated, the true confidence level of the interval may be very different from 90%

Answer 20

True. If the assumptions

are false the true confidence level may be very different from what is stated

Question 21

All else being equal, the width of a confidence interval decreases as the confidence level increases.

Answer 21

False. If we want greater confidence that the interval captures the parameter, we must cover more ground and have a wider interval.

Question 22

All else being equal, the margin of error decreases as the confidence level increases.

Answer 22

False. The margin of error increases as the confidence level increases.

Question 23

All else being equal, the standard error of the sample mean decreases as the confidence level of
the interval increases

Answer 23

False. SE(X¯) = √s/n, which does not involve the confidence level.

Question 24

All else being equal, the confidence level of an interval increases as the sample size increases

Answer 24

False. The confidence level (1 − α) and sample size (n) are not related.