Question 1

A researcher estimates the 95% CI for a sample with a mean of M = 3.26 and a standard error ( $\sigma$_M)of 0.91.What is the upper confidence limit for this interval? A) 1.48 B) 2.35 C) 4.17 D) 5.04

Accepted Answer

The upper confidence limit is calculated as the mean plus the margin of error. For a 95% CI, the margin of error is 1.96 times the standard error. So, 3.26 + (1.96 * 0.91) = 5.04.

Question 2

If the null hypothesis is inside the confidence interval,then the decision was likely to ______ using hypothesis testing.
A) reject the null hypothesis
B) retain the null hypothesis

Accepted Answer

If the null hypothesis is inside the confidence interval, it means that the sample result is not significantly different from the null hypothesis at the chosen level of significance. Therefore, we fail to reject the null hypothesis (retain it) as there is not enough evidence to reject it.

Question 3

Which of the following best describes the goal of estimation?
A) to determine the extent to which a result is significant
B) to estimate the significance of a result
C) to narrow in on the true population mean by defining limits within which it is likely to be contained
D) to determine the extent to which a result is significant and to estimate the significance of a result

Accepted Answer

The goal of estimation is to estimate population parameters such as mean, proportion, or variance, and to define a range of values (confidence interval) within which the true parameter value is likely to lie. Option C correctly describes the goal of estimation. Option A and B do not fully capture the purpose of estimation, which is not only to determine or estimate significance but rather to estimate the population parameter itself. Option D is redundant and unnecessarily combines A and B, which are similar.

Question 4

A researcher estimates the 90% CI for a sample with a mean of M = 8.9 and a standard error ( $\sigma$_M)of 2.1.What is the confidence interval at this level of confidence? A) 90% CI 4.8, 13.0 B) 90% CI 5.5, 12.4 C) 90% CI 6.8, 11.0 D) There is not enough information to answer this question.

Accepted Answer

The formula for calculating the confidence interval at a specific confidence level is:
CI = M ± Z*(SE)
where M is the sample mean, SE is the standard error, and Z is the critical value for the given confidence level.

For a 90% confidence level, the Z-value is 1.645. 
Thus, the confidence interval is: 
CI = 8.9 ± 1.645*(2.1) = (5.5, 12.4)

Therefore, the best choice is B.

Question 5

If the value stated by a null hypothesis is ______ the confidence interval,then the decision would likely be to reject the null hypothesis.
A) inside
B) outside

Accepted Answer

If the value stated by the null hypothesis falls outside of the confidence interval, it suggests that the null hypothesis is unlikely to be true and there is evidence against it. Therefore, the decision would likely be to reject the null hypothesis.

Question 6

A statistical procedure in which a sample statistic is used to estimate the value of an unknown population parameter is called ______.
A) an educated guess
B) appropriation
C) estimation
D) significance testing

Accepted Answer

The definition provided matches the concept of estimation, which is the process of using a sample to derive a plausible value for an unknown population parameter. Option A is not accurate because estimation is not based on guesswork but on evidence-based inference. Option B is not fitting as an answer because it is not related to statistical procedures that involve estimating a population parameter using a sample statistic. Option D involves a different statistical procedure - hypothesis testing - which is not the same as estimating a parameter.

Question 7

Which type of error is used to compute the confidence interval for one sample selected from a 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

To compute the confidence interval for one sample selected from a population with an unknown variance, we use the estimated standard error, which is calculated using the sample standard deviation.

Question 8

A researcher estimates the 95% CI for a sample with a mean of M = 3.26 and a standard error ( $\sigma$_M)of 0.91.What is the lower confidence limit for this interval? A) 1.48 B) 2.35 C) 4.17 D) 5.04

Accepted Answer

To find the lower confidence limit for the 95% CI, we need to subtract the margin of error from the sample mean. The margin of error is equal to 1.96 times the standard error:

Margin of error = 1.96 * 0.91 = 1.78

Lower confidence limit = M - margin of error = 3.26 - 1.78 = 1.48

Therefore, the answer is A.

Question 9

A researcher concludes that stress levels are higher following a major versus a minor traffic accident (95% confidence interval [CI] 1.86-3.02).If the null hypothesis stated that there would be no difference (null hypothesis: $\mu$ = 0),then what is the effect size for this confidence interval?
A) Between 1.86% and 3.02% of the variability in stress levels can be accounted for by type of traffic accident.
B) Ratings of stress shifted more than 1.86 points in the population.
C) Ratings of stress shifted between 1.86 and 3.02 points in the population.
D) There is not enough information to answer this question.

Accepted Answer

The effect size for this confidence interval would be the range between the upper and lower bounds of the CI, which is 1.86-3.02. Therefore, ratings of stress shifted between 1.86 and 3.02 points in the population.

Question 10

A researcher reports that college students consume an average of 3.6 alcoholic drinks per week.What is the interval estimate in this example?
A) 3.6
B) The interval estimate is not given.

Accepted Answer

The question asks for the interval estimate, which is not provided in the given information. The average consumption of 3.6 drinks per week only gives us the point estimate, not the interval estimate.

Question 11

If the value stated by a null hypothesis is ______ the confidence interval,then the decision would have likely been to retain the null hypothesis.
A) inside
B) outside

Accepted Answer

If the value stated by the null hypothesis is inside the confidence interval, then it means that the observed data is consistent with the null hypothesis. Therefore, we would fail to reject the null hypothesis and retain it as the most plausible explanation for the observed data.

Question 12

Which of the following explains why point estimation can be a useful procedure to estimate a population mean?
A) It defines the range of scores within which the population mean is likely to be contained.
B) The sample mean is equal to the population mean on average.
C) The sample mean is an unbiased estimator of the population mean.
D) The sample mean is equal to the population mean on average and the sample mean is an unbiased estimator of the population mean.

Accepted Answer

Point estimation involves using a single value (the sample mean) to estimate the population parameter (the population mean). The sample mean is a good estimator of the population mean because on average it will be equal to the population mean. Additionally, the sample mean is an unbiased estimator, meaning that it is not systematically over- or underestimates the population mean. Therefore, D is the best answer as it combines both of these reasons.

Question 13

Which type of error is used to compute the confidence interval for one sample selected from a population with a known 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 one sample selected from a population with a known variance, we use the standard error.

Question 14

A researcher estimates the 95% CI for a sample with a mean of M = 9.0 and a standard error ( $\sigma$_M)of 1.03.What is the confidence interval at this level of confidence? A) 95% CI 7.3, 10.7 B) 95% CI 8.0, 10.0 C) 95% CI 7.0, 11.0 D) There is not enough information to answer this question.

Accepted Answer

The answer of A researcher estimates the 95% CI for...

Question 15

If the null hypothesis is outside the confidence interval,then the decision was likely to ______ using hypothesis testing.
A) reject the null hypothesis
B) retain the null hypothesis

Accepted Answer

If the null hypothesis is outside the confidence interval, it means that the observed results are unlikely to have occurred by chance under the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.

Question 16

A point estimate is typically reported with an interval estimate.Why?
A) Using only a point estimate is associated with low certainty.
B) The interval estimate gives researchers a higher level of confidence.
C) The interval estimate adds certainty to the estimate of the population mean.
D) All of these.

Accepted Answer

Using only a point estimate can be associated with low certainty as it provides only one value as an estimate of the parameter. The interval estimate provides a range within which the parameter is likely to fall, increasing the level of confidence researchers have in the estimate. Therefore, using both a point estimate and an interval estimate can help to add certainty to the estimate of the population mean.

Question 17

A researcher compares the height of male executives in the United States to the average height of males ($\mu$ = 67 in.).He determines that the average height of male executives is 70 in.(95% confidence interval [CI] 68-72).Based on this result,what would the decision have been for a hypothesis test?
A) reject the null hypothesis
B) retain the null hypothesis
C) there is not enough information to answer this question

Accepted Answer

The 95% confidence interval does not include the average height of the general male population (67 in.), which indicates that the difference between the two groups is statistically significant. Therefore, the null hypothesis of "there is no difference in height between male executives and the average male population" would be rejected in favor of the alternative hypothesis of "male executives are taller than the average male population."

Question 18

The confidence interval for samples selected from one or two populations with an unknown variance is computed using critical values from the t table.This is true for which of the following types of samples?
A) one sample
B) two-independent sample
C) related samples
D) all of these

Accepted Answer

The t-table is used to compute confidence intervals for all three types of samples: one sample, two-independent samples, and related samples.

Question 19

A researcher reports with 90% confidence that 31% to 37% of Americans believe in ghosts.What is the point estimate for this interval?
A) 31%
B) 34%
C) 37%
D) 31% to 37%

Accepted Answer

The point estimate is the middle value of the interval, which is the average of the lower and upper bounds. Thus, the point estimate is (31% + 37%) / 2 = 34%.

Question 20

The confidence interval for one sample selected from a population with a known variance is computed using a critical value for which type of test?
A) z test
B) t test
C) none
D) both A and B

Accepted Answer

When the population variance is known and the sample size is large (n > 30), a z-test is appropriate. In this case, the confidence interval would be calculated using a critical value from the standard normal distribution.

Quiz 11: Estimation and Confidence Intervals

A researcher estimates the 95% CI for a sample with a mean of M = 3.26 and a standard error ( $\sigma$ _M) of 0.91.What is the upper confidence limit for this interval?

If the null hypothesis is inside the confidence interval,then the decision was likely to ______ using hypothesis testing.

Which of the following best describes the goal of estimation?

A researcher estimates the 90% CI for a sample with a mean of M = 8.9 and a standard error ( $\sigma$ _M) of 2.1.What is the confidence interval at this level of confidence?

If the value stated by a null hypothesis is ______ the confidence interval,then the decision would likely be to reject the null hypothesis.

A statistical procedure in which a sample statistic is used to estimate the value of an unknown population parameter is called ______.

Which type of error is used to compute the confidence interval for one sample selected from a population with an unknown variance?

A researcher estimates the 95% CI for a sample with a mean of M = 3.26 and a standard error ( $\sigma$ _M) of 0.91.What is the lower confidence limit for this interval?

A researcher concludes that stress levels are higher following a major versus a minor traffic accident (95% confidence interval [CI] 1.86-3.02) .If the null hypothesis stated that there would be no difference (null hypothesis: $\mu$ = 0) ,then what is the effect size for this confidence interval?

A researcher reports that college students consume an average of 3.6 alcoholic drinks per week.What is the interval estimate in this example?

If the value stated by a null hypothesis is ______ the confidence interval,then the decision would have likely been to retain the null hypothesis.

Which of the following explains why point estimation can be a useful procedure to estimate a population mean?

Which type of error is used to compute the confidence interval for one sample selected from a population with a known variance?

A researcher estimates the 95% CI for a sample with a mean of M = 9.0 and a standard error ( $\sigma$ _M) of 1.03.What is the confidence interval at this level of confidence?

If the null hypothesis is outside the confidence interval,then the decision was likely to ______ using hypothesis testing.

A point estimate is typically reported with an interval estimate.Why?

The confidence interval for samples selected from one or two populations with an unknown variance is computed using critical values from the t table.This is true for which of the following types of samples?

A researcher reports with 90% confidence that 31% to 37% of Americans believe in ghosts.What is the point estimate for this interval?

The confidence interval for one sample selected from a population with a known variance is computed using a critical value for which type of test?