Question 1

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of M₁ - M₂ = 8.8 and an estimated standard error for the difference (S_M1_-_M2)of 1.8.What is the lower confidence limit for this interval?

Accepted Answer

The lower confidence limit for an 80% CI can be calculated using the formula: mean - (Z * standard error), where Z is the Z-score corresponding to the desired confidence level. For an 80% CI, the Z-score is approximately 1.28. Thus, the calculation is 8.8 - (1.28 * 1.8) = 8.8 - 2.304 = 6.496, which rounds to 6.4.

Question 2

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

Accepted Answer

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

Question 3

Which of the following words best describes certainty?

Accepted Answer

Confidence is the best word to describe certainty because it denotes a sense of assurance or trust in a particular outcome, idea, or belief.

Question 4

In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of M₁ - M₂ = 10.7 and an estimated standard error for the difference (S_M1_-_M2)of 2.9.What is the confidence interval at this level of confidence?

Accepted Answer

Using the formula:

CI = (difference in means) ± (critical value) * (standard error)

We can calculate the critical value for a 90% confidence interval with 12 degrees of freedom (14 - 2) using a t-distribution table or calculator as approximately 1.782.

Plugging in the given values:

CI = 10.7 ± 1.782 * 2.9

CI = 10.7 ± 5.17

CI = (10.7 - 5.17, 10.7 + 5.17)

CI = (5.53, 16.87)

So the 90% confidence interval for the difference in means is (5.53, 16.87). Therefore, the answer is B: 90% CI 5.5, 15.9.

Question 5

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 (S_M)of 0.3.What is the confidence interval at this level of confidence?

Accepted Answer

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

Question 6

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

Accepted Answer

To find the upper confidence limit, we need to use the formula: Upper limit = M_D + (critical value * standard error) The critical value for a 90% confidence interval with 26 degrees of freedom is 1.699. Plugging in the values, we get: Upper limit = 0.6 + (1.699 * 0.1) Upper limit = 0.77 Therefore, the answer is A) 0.77.

Question 7

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?

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 8

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of M₁ - M₂ = 8.8 and an estimated standard error for the difference (S_M1_-_M2)of 1.8.What is the upper confidence limit for this interval?

Accepted Answer

The upper confidence limit is calculated as the mean difference plus the margin of error. The margin of error is the product of the critical value (z-score for 80% CI is approximately 1.28) and the standard error. Thus, 8.8 + (1.28 * 1.8) = 11.2.

Question 9

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 (S_M)of 1.6.What is the upper confidence limit for this interval?

Accepted Answer

The upper confidence limit is calculated as the sample mean plus the margin of error. The margin of error is the product of the critical t-value (approximately 2.093 for 19 degrees of freedom at 95% confidence) and the standard error. Thus, 5.4 + (2.093 * 1.6) = 8.8.

Question 10

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

Accepted Answer

A smaller level of confidence results in a narrower confidence interval, making the estimate more precise.

Question 11

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

Accepted Answer

The 90% confidence interval is calculated using the formula: M_D ± (t * S_MD). With 16 degrees of freedom (n-1=17-1), the t-value for 90% CI is approximately 1.746. Thus, the interval is 7 ± (1.746 * 2.2), which results in 3.2 to 10.8.

Question 12

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

Accepted Answer

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

Question 13

Which of the following is a characteristic of confidence intervals?

Accepted Answer

Confidence intervals are used to estimate a population parameter. As the level of confidence increases, the precision of the estimate decreases because a wider range of values is considered. When the level of confidence decreases, the precision of the estimate increases because a narrower range of values is considered. Therefore, the less certain the estimate (lower confidence level), the more precise it is, and the more certain the estimate (higher confidence level), the less precise it is.

Question 14

In a sample of 30 participants,a researcher estimates the 95% CI for a sample with a mean of M₁ - M₂ = 0.7 and an estimated standard error for the difference (S_M1_-_M2)of 0.2.What is the confidence interval at this level of confidence?

Accepted Answer

The 95% confidence interval is calculated as the mean difference ± (critical value * standard error). For a 95% CI, the critical value is approximately 1.96. Thus, 0.7 ± (1.96 * 0.2) gives the interval 0.3 to 1.1.

Question 15

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

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 16

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?

Accepted Answer

When computing the confidence interval for two independent samples selected from at least one population with an unknown variance, the estimated standard error for the difference is used. This is because the difference between the sample means (which is used to compute the confidence interval) has its own variability, and this variability needs to be taken into account when estimating the confidence interval. The estimated standard error for the difference is calculated as the square root of the sum of the variances of the two samples divided by their respective sample sizes.

Question 17

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

Accepted Answer

The 99% confidence interval is calculated as M_D ± (critical t-value) * S_MD. With 19 degrees of freedom (n-1), the critical t-value is approximately 2.861. Thus, the interval is 3.7 ± (2.861 * 0.2), which is approximately 3.1 to 4.3.

Question 18

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

Accepted Answer

Reducing the level of confidence from 99% to 90% results in a narrower confidence interval, making the estimate more precise. This is because a lower confidence level means accepting a higher risk of error, which allows for a more specific range of values.

Question 19

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 (S_M)of 1.6.What is the lower confidence limit for this interval?

Accepted Answer

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

Question 20

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 (S_M)of 4.7.What is the confidence interval at this level of confidence?

Accepted Answer

The 80% confidence interval is calculated as the sample mean plus or minus the margin of error, which is the product of the estimated standard error and the critical value from the t-distribution with 11 degrees of freedom (n-1) and a confidence level of 80%. The critical value is 1.314, so the margin of error is 4.7 * 1.314 = 6.183. The confidence interval is therefore 22.3 +/- 6.183, or (15.9, 28.7).

Quiz 11: Estimation and Confidence Intervals

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of M₁ - M₂ = 8.8 and an estimated standard error for the difference (S_M1_-_M2) of 1.8.What is the lower confidence limit for this interval?

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

Which of the following words best describes certainty?

In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of M₁ - M₂ = 10.7 and an estimated standard error for the difference (S_M1_-_M2) of 2.9.What is the confidence interval at this level of confidence?

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 (S_M) of 0.3.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 M_D = 0.6 and an estimated standard error for the difference scores (S_MD) of 0.1.What is the upper confidence limit for this interval?

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 18 participants,a researcher estimates the 80% CI for a sample with a mean of M₁ - M₂ = 8.8 and an estimated standard error for the difference (S_M1_-_M2) 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 (S_M) of 1.6.What is the upper confidence limit for this interval?

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

In a sample of 17 participants,a researcher estimates the 90% CI for a sample with a mean of M_D = 7 and an estimated standard error for the difference scores (S_MD) of 2.2.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 M_D = 0.6 and an estimated standard error for the difference scores (S_MD) of 1.1.What is the upper confidence limit for this interval?

Which of the following is a characteristic of confidence intervals?

In a sample of 30 participants,a researcher estimates the 95% CI for a sample with a mean of M₁ - M₂ = 0.7 and an estimated standard error for the difference (S_M1_-_M2) of 0.2.What is the confidence interval at this level of confidence?

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

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

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

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 (S_M) of 1.6.What is the lower confidence limit for this interval?

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 (S_M) of 4.7.What is the confidence interval at this level of confidence?

Quiz 11: Estimation and Confidence Intervals

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of M1 - M2 = 8.8 and an estimated standard error for the difference (SM1 - M2) of 1.8.What is the lower confidence limit for this interval?

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

Which of the following words best describes certainty?

In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of M1 - M2 = 10.7 and an estimated standard error for the difference (SM1 - M2) of 2.9.What is the confidence interval at this level of confidence?

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 (SM) of 0.3.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 MD = 0.6 and an estimated standard error for the difference scores (SMD) of 0.1.What is the upper confidence limit for this interval?

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 18 participants,a researcher estimates the 80% CI for a sample with a mean of M1 - M2 = 8.8 and an estimated standard error for the difference (SM1 - M2) 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 (SM) of 1.6.What is the upper confidence limit for this interval?

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

In a sample of 17 participants,a researcher estimates the 90% CI for a sample with a mean of MD = 7 and an estimated standard error for the difference scores (SMD) of 2.2.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 MD = 0.6 and an estimated standard error for the difference scores (SMD) of 1.1.What is the upper confidence limit for this interval?

Which of the following is a characteristic of confidence intervals?

In a sample of 30 participants,a researcher estimates the 95% CI for a sample with a mean of M1 - M2 = 0.7 and an estimated standard error for the difference (SM1 - M2) of 0.2.What is the confidence interval at this level of confidence?

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

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

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

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 (SM) of 1.6.What is the lower confidence limit for this interval?

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 (SM) of 4.7.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 M₁ - M₂ = 8.8 and an estimated standard error for the difference (S_M1_-_M2) of 1.8.What is the lower confidence limit for this interval?

In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of M₁ - M₂ = 10.7 and an estimated standard error for the difference (S_M1_-_M2) of 2.9.What is the confidence interval at this level of confidence?

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 (S_M) of 0.3.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 M_D = 0.6 and an estimated standard error for the difference scores (S_MD) of 0.1.What is the upper confidence limit for this interval?

In a sample of 18 participants,a researcher estimates the 80% CI for a sample with a mean of M₁ - M₂ = 8.8 and an estimated standard error for the difference (S_M1_-_M2) 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 (S_M) of 1.6.What is the upper confidence limit for this interval?

In a sample of 17 participants,a researcher estimates the 90% CI for a sample with a mean of M_D = 7 and an estimated standard error for the difference scores (S_MD) of 2.2.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 M_D = 0.6 and an estimated standard error for the difference scores (S_MD) of 1.1.What is the upper confidence limit for this interval?

In a sample of 30 participants,a researcher estimates the 95% CI for a sample with a mean of M₁ - M₂ = 0.7 and an estimated standard error for the difference (S_M1_-_M2) of 0.2.What is the confidence interval at this level of confidence?

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

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 (S_M) of 1.6.What is the lower confidence limit for this interval?

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 (S_M) of 4.7.What is the confidence interval at this level of confidence?