Question 1

Which type of error is used to compute the confidence interval for two related samples selected from at least one population with an unknown variance?
A)standard error
B)estimated standard error
C)estimated standard error for the difference
D)estimated standard error for the difference scores

Accepted Answer

The correct answer is D) estimated standard error for the difference scores. This is because when computing the confidence interval for two related samples (e.g., matched pairs or repeated measures), the variability of the difference scores between pairs is what matters, not the variability within each sample. Since the population variance is unknown, an estimate based on the sample data is used, hence "estimated standard error for the difference scores."

Question 2

In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of  = 10.7 and an estimated standard error for the difference (  )of 2.9.What is the confidence interval at this level of confidence?
A)90% CI 4.4,17.0
B)90% CI 5.5,15.9
C)90% CI 7.8,13.6
D)There is not enough information to answer this question.

Accepted Answer

Using the formula for calculating the confidence interval:
CI = mean +/- (z-score critical value * standard error)
At 90% confidence level, the z-score critical value is 1.645
So, CI = 10.7 +/- (1.645 * 2.9)
CI = 10.7 +/- 4.783
CI = (10.7 - 4.783) to (10.7 + 4.783)
CI = 5.917 to 15.483
Therefore, the 90% CI is 5.5 to 15.9 (rounded to one decimal place). The correct answer is B.

Question 3

A researcher increases his level of confidence from 90% to 95%.What will happen to the precision of his estimate?
A)The estimate will be more precise.
B)The estimate will be less precise.
C)The precision of his estimate will not change.
D)It depends on the size of the population.

Accepted Answer

Increasing the level of confidence generally requires widening the confidence interval, which makes the estimate less precise.

Question 4

Which of the following is a characteristic of confidence intervals?
A)The less certain an estimate,the more precise the estimate.
B)The more certain an estimate,the less precise the estimate.
C)both A and B

Accepted Answer

Confidence intervals are based on the level of certainty or probability of the estimate. The width of the confidence interval will decrease as the level of certainty or probability increases, resulting in a more precise estimate. However, if there is less certainty or probability, the width of the interval will increase, resulting in a less precise estimate. Therefore, both options A and B are true characteristics of confidence intervals.

Question 5

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of  = 8.8 and an estimated standard error for the difference (  )of 1.8.What is the upper confidence limit for this interval?
A)6.4
B)7.0
C)10.6
D)11.2

Accepted Answer

The answer of In a sample of 18 participants,a researcher...

Question 6

In a sample of 20 participants,a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error (  )of 1.6.What is the upper confidence limit for this interval?
A)2.1
B)3.8
C)7.0
D)8.8

Accepted Answer

The answer of In a sample of 20 participants,a researcher...

Question 7

In a sample of 26 participants,a researcher estimates the 90% CI for a sample with a mean of  = 0.6 and an estimated standard error for the difference scores (  )of 0.1.What is the upper confidence limit for this interval?
A)0.77
B)-0.5
C)1.7
D)2.5

Accepted Answer

The answer of In a sample of 26 participants,a researcher...

Question 8

A researcher reduces her level of confidence from 99% to 90%.What will happen to the precision of her estimate?
A)The estimate will be more precise.
B)The estimate will be less precise.
C)The precision of her estimate will not change.
D)It depends on the size of the population.

Accepted Answer

When the researcher reduces her confidence level, the margin of error in her estimate also decreases, which means the estimate becomes more precise. Therefore, choice A is the correct answer.

Question 9

The smaller the level of confidence,the ________ precise the estimate.
A)more
B)less

Accepted Answer

The answer of The smaller the level of confidence,the ________...

Question 10

The larger the level of confidence,the ________ precise the interval estimate.
A)more
B)less

Accepted Answer

A larger level of confidence means that we want to be more certain that our interval estimate contains the true parameter value. To achieve this, we widen the interval, making it less precise.

Question 11

In a sample of 12 participants,a researcher estimates the 80% CI for a sample with a mean of M = 22.3 and an estimated standard error (  )of 4.7.What is the confidence interval at this level of confidence?
A)80% CI 12.1,32.5
B)80% CI 17.6,27.0
C)80% CI 15.9,28.7
D)There is not enough information to answer this question.

Accepted Answer

The answer of In a sample of 12 participants,a researcher...

Question 12

In a sample of 17 participants,a researcher estimates the 90% CI for a sample with a mean of  = 7 and an estimated standard error for the difference scores (  )of 2.2.What is the confidence interval at this level of confidence?
A)90% CI 2.4,11.6
B)90% CI 3.2,10.8
C)90% CI 4.8,9.2
D)There is not enough information to answer this question.

Accepted Answer

The formula to calculate the confidence interval for a mean is:
CI = x̄ ± t*(SE)
where x̄ is the sample mean, t is the critical value from the t-distribution table based on the degrees of freedom (df = n-1) and level of confidence (0.9 for 90% CI), and SE is the estimated standard error of the mean.
Substituting the given values:
CI = 7 ± 1.740*(2.2)
CI = 7 ± 3.832
CI = (7-3.832, 7+3.832)
CI = (3.168, 10.832)
Therefore, the 90% CI is 3.2 to 10.8, which is closest to option B.

Question 13

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of  = 8.8 and an estimated standard error for the difference (  )of 1.8.What is the lower confidence limit for this interval?
A)6.4
B)7.0
C)10.6
D)11.2

Accepted Answer

The answer of In a sample of 18 participants,a researcher...

Question 14

In a sample of 30 participants,a researcher estimates the 95% CI for a sample with a mean of  = 0.7 and an estimated standard error for the difference (  )of 0.2.What is the confidence interval at this level of confidence?
A)95% CI 0.4,1.0
B)95% CI 0.5,0.9
C)95% CI 0.3,1.1
D)There is not enough information to answer this question.

Accepted Answer

The answer of In a sample of 30 participants,a researcher...

Question 15

In a sample of 26 participants,a researcher estimates the 90% CI for a sample with a mean of  = 0.6 and an estimated standard error for the difference scores (  )of 1.1.What is the upper confidence limit for this interval?
A)-1.3
B)-0.5
C)1.7
D)2.5

Accepted Answer

The answer of In a sample of 26 participants,a researcher...

Question 16

In a sample of 20 participants,a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error (  )of 1.6.What is the lower confidence limit for this interval?
A)2.1
B)3.8
C)7.0
D)8.8

Accepted Answer

The answer of In a sample of 20 participants,a researcher...

Question 17

In a sample of 20 participants,a researcher estimates the 99% CI for a sample with a mean of  = 3.7 and an estimated standard error for the difference scores (  )of 0.2.What is the confidence interval at this level of confidence?
A)99% CI 3.5,3.9
B)99% CI 3.2,4.2
C)99% CI 3.1,4.3
D)There is not enough information to answer this question.

Accepted Answer

The answer of In a sample of 20 participants,a researcher...

Question 18

Which type of error is used to compute the confidence interval for two independent samples selected from at least one population with an unknown variance?
A)standard error
B)estimated standard error
C)estimated standard error for the difference
D)estimated standard error for the difference scores

Accepted Answer

When computing the confidence interval for two independent samples selected from at least one population with an unknown variance, we use the estimated standard error for the difference between the two sample means. This is because we do not know the population variance(s), so we must estimate it (or them) using the sample variances. The estimated standard error for the difference takes into account the sample sizes, sample variances, and the fact that we are computing the difference between two sample means.

Question 19

In a sample of 28 participants,a researcher estimates the 95% CI for a sample with a mean of M = 1.5 and an estimated standard error (  )of 0.3.What is the confidence interval at this level of confidence?
A)95% CI 1.0,2.0
B)95% CI 1.2,1.8
C)95% CI 0.9,2.1
D)There is not enough information to answer this question.

Accepted Answer

The answer of In a sample of 28 participants,a researcher...

Question 20

Which of the following words best describes certainty?
A)inferential
B)significance
C)precision
D)confidence

Accepted Answer

Certainty is a state of being confident or sure about something. Therefore, the word that best describes certainty is "confidence."

Quiz 11: One-Way Analysis of Variance: Between- Subjects and Within- Subjects Repeated- Measures Designs

Which type of error is used to compute the confidence interval for two related samples selected from at least one population with an unknown variance?

In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of = 10.7 and an estimated standard error for the difference ( ) of 2.9.What is the confidence interval at this level of confidence?

A researcher increases his level of confidence from 90% to 95%.What will happen to the precision of his estimate?

Which of the following is a characteristic of confidence intervals?

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of = 8.8 and an estimated standard error for the difference ( ) of 1.8.What is the upper confidence limit for this interval?

In a sample of 20 participants,a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error ( ) of 1.6.What is the upper confidence limit for this interval?

In a sample of 26 participants,a researcher estimates the 90% CI for a sample with a mean of = 0.6 and an estimated standard error for the difference scores ( ) of 0.1.What is the upper confidence limit for this interval?

A researcher reduces her level of confidence from 99% to 90%.What will happen to the precision of her estimate?

The smaller the level of confidence,the ________ precise the estimate.

The larger the level of confidence,the ________ precise the interval estimate.

In a sample of 12 participants,a researcher estimates the 80% CI for a sample with a mean of M = 22.3 and an estimated standard error ( ) of 4.7.What is the confidence interval at this level of confidence?

In a sample of 17 participants,a researcher estimates the 90% CI for a sample with a mean of = 7 and an estimated standard error for the difference scores ( ) of 2.2.What is the confidence interval at this level of confidence?

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of = 8.8 and an estimated standard error for the difference ( ) of 1.8.What is the lower confidence limit for this interval?

In a sample of 30 participants,a researcher estimates the 95% CI for a sample with a mean of = 0.7 and an estimated standard error for the difference ( ) of 0.2.What is the confidence interval at this level of confidence?

In a sample of 26 participants,a researcher estimates the 90% CI for a sample with a mean of = 0.6 and an estimated standard error for the difference scores ( ) of 1.1.What is the upper confidence limit for this interval?

In a sample of 20 participants,a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error ( ) of 1.6.What is the lower confidence limit for this interval?

In a sample of 20 participants,a researcher estimates the 99% CI for a sample with a mean of = 3.7 and an estimated standard error for the difference scores ( ) of 0.2.What is the confidence interval at this level of confidence?

Which type of error is used to compute the confidence interval for two independent samples selected from at least one population with an unknown variance?

In a sample of 28 participants,a researcher estimates the 95% CI for a sample with a mean of M = 1.5 and an estimated standard error ( ) of 0.3.What is the confidence interval at this level of confidence?

Which of the following words best describes certainty?