Deck 7: Point Estimation and Confidence Intervals

Question 1

The estimates of the mean and proportion that are obtained from a sample are referred to as ______ of the same values in the population.

A) sample statistics
B) point estimates
C) population parameters
D) confidence levels

Answer 1

B

Question 2

A confidence interval is ______.

A) the lower and upper boundaries of the confidence interval
B) a statistical interval around a point estimate (the mean) that provides a specified level of confidences for the true population parameter
C) a range of numbers that tells us the probability that our estimate is wrong
D) range of values for a variable that has a stated probability of containing an unknown population mean

Answer 2

B

Question 3

A confidence interval is equal to Confidenceinterval $=$ pointestimate $\pm$ ________ $?$

A) the variance
B) mean deviation
C) margin of error
D) alpha

Answer 3

margin of error

Question 4

If a research reports "The margin of sampling error is $\pm$ 8 points at the 95% confidence level", this means that ______.

A) they are 95% confident that their exact point estimate is correct
B) they are 95% confident that the true population parameter is included in the intervals of $\pm$ 8 points
C) they are 95% confident that the true population parameter is included in the intervals of $\pm$ 4 points
D) they are 95% they are correct

Question 5

As sample sizes ______, the sample means of the sampling distribution cluster more tightly around the population mean.

A) increases
B) decreases
C) stays the same
D) changes

Question 6

For a sample of 29 individuals, we would rely on the ______.

A) z-distribution
B) central limit theorem
C) t-distribution
D) confidence limits

Question 7

For a sample of 30 individuals, we would rely on the ______.

A) z-distribution
B) square root of the variance
C) t-distribution
D) confidence limits

Question 8

In the equation for the standard deviation of the sampling distribution, $\frac{s}{\sqrt{n}}$ , where s is the standard deviation and n is the sample size, how could one get more precise estimates that differ less from one another?

A) increase s to expand the distribution
B) increase the sample size (n) because as the denominator increase the resulting value decreases
C) decrease the sample size (n) because as the denominator decreases the resulting value decreases
D) collect data that are not skewed

Question 9

In the equation for confidence intervals, $\bar{X} \pm z_{a}\left(\frac{s}{\sqrt{n}}\right)$ , $Z_{a}$ corresponds to ______.

A) the alpha we are using (the level of confidence)
B) the standard deviation of our sample
C) the variance of our sample
D) the lower limit of our confidence interval

Question 10

A confidence level of 90% is what size alpha?

A) .001
B) .01
C) .05
D) .10

Question 11

A confidence level of 95% is what size alpha?

A) .001
B) .01
C) .05
D) .10

Question 12

A z-score of 2.58 corresponds to what size alpha?

A) .001
B) .01
C) .05
D) .10

Question 13

A z-score of 1.95 corresponds to what size alpha?

A) .001
B) .01
C) .05
D) .10

Question 14

As compared to a z-distribution, a t-distribution is ______.

A) flatter
B) more precise
C) positively skewed
D) negatively skewed

Question 15

Which equation is used to find the degrees of freedom in a sample of 29 individuals?

A) $n-2$
B) $n-$ -3
C) $n-1$
D) $n-n$

Question 16

At what sample size are the t- and z-distributions identical?

A) 120
B) 100
C) 30
D) 50

Question 17

______ are the lower and upper boundaries of the confidence interval.

A) Point estimates
B) Population estimates
C) Confidence limits
D) Confidence levels

Question 18

The following equation, $\sigma_{p}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ , is used to compute ______.

A) standard error of a small sample
B) standard error of the proportion
C) variance of the proportion
D) confidence limits of proportion

Question 19

Point estimates are the estimate of the mean and proportion that we obtained from a sample.

Question 20

The 95% confidence interval will be wider than the 99% confidence interval.

Question 21

When calculating the confidence interval for a small sample the t-distribution is utilized to obtain the critical value.

Question 22

A researcher will have more confidence that the sample mean estimates the unknown population mean when the sample size is larger.

Question 23

Discuss the difference between the 95% and the 99% confidence intervals.

Question 24

On a single graph, draw a t-distribution. Then overlay the t-distribution with a z-distribution. How are they different? What implications do these differences have for sampling error, estimates, and confidence intervals?