Quiz #7 - Margin of Error & Confidence Intervals Flashcards
A researcher is interested in students’ anxiety about statistics. There are 200 students in the class. The confidence interval obtained for the average statistics anxiety score is [9,11]. Which of the following is true? Choose ALL that apply.
A: The margin of error for students’ statistics anxiety scores is 1
B: The mean of students’ statistics anxiety scores is 10
C: The standard deviation of students’ anxiety scores is 2
D: The margin of error for students’ statistics anxiety scores is 2
A: The margin of error for students’ statistics anxiety scores is 1
- To find this answer you need to subtract the lower bound from the upper bound and then divide by 2. This will give you the margin of error in this case. You can figure this out by referencing the confidence interval formula.
B: The mean of students’ statistics anxiety scores is 10
- To find this answer you can also reference the confidence interval formula. Now that we know the margin of error (we found it for “A”) we can plug it into the formula (sample mean/estimate +- margin of error).
x - 1 = 9 (lower bound) solve for x (add 1 on both sides)
x + 1 = 11 (upper bound) solve for x (subtract 1 on both sides). Alternatively, you can add the upper bound and lower bound together and divide by 2.
Confidence interval formula:
sample mean/estimate +- margin of error
[lower bound, upper bound]
A clinical researcher estimates the rate of clinical depression among new mothers at 18% based on a dataset of 100 new mothers. This researcher is 95% confident that the range from 17% to 19% contains the true proportion of depressed mothers in the population. We use a t distribution as the sampling distribution. Based on this information, we can obtain/calculate ________. Choose ALL that apply.
A: Confidence interval
B: Critical value
C: Margin of error
D: Standard error
A: Confidence interval
B: Critical value
C: Margin of error
D: Standard error
A researcher finds the sample mean on a happiness scale for students is 15. Which of the following will produce the smallest confidence interval (i.e., the smallest range)? Select one:
A: Sample size has no impact on the confidence interval
B: A sample size of 150
C: A sample size of 250
C: A sample size of 250
The estimates from many random samples follow a normal distribution. This fact allows us to determine that 95% of all random samples will yield estimates within plus or minus 1.96 _______ from the _______.
A: Standard error units, sample estimate
B: Standard error units, population parameter
C: Standard deviation units, sample estimate
D: Standard deviation units, population parameter
B: Standard error units, population parameter
To construct a confidence interval, we need to calculate it as plus or minus 1.96 _______ from the _______ (using the normal distribution as the sampling distribution).
A: Standard error units, population parameter
B: Standard error units, sample estimate
C: Standard deviation units, population parameter
D: Standard deviation units, sample estimate
B: Standard error units, sample estimate
A study of exam anxiety at UCLA provides a mean of 60 with a 95% confidence interval of 50 to 70. Which of the following is a correct interpretation of the confidence interval?
A: We are 95% confident that the interval from 50 to 70 includes the sample mean
B: The true population average exam anxiety in the entire population must fall somewhere between 50 to 70
C: We are 95% confident that the range from 50 to 70 includes the true population average exam anxiety in the entire population of students
D: If the researcher repeated the study with a new sample, there is a 95% chance that the new estimate would fall between 50 to 70
E: 95% of all random samples would yield estimates ranging from 50 to 70
C: We are 95% confident that the range from 50 to 70 includes the true population average exam anxiety in the entire population of students
Holding the standard error of an estimate constant, which t-distribution would result in the largest margin of error for a 95% confidence interval:
A: A t distribution with 16 degrees of freedom
B: A t distribution with 24 degrees of freedom
C: A t distribution with 8 degrees of freedom
C: A t distribution with 8 degrees of freedom
There are three researchers who are calculating confidence intervals for their sample mean estimate. Researcher A has 20 participants in their sample, Researcher B has 50 participants, and Researcher C has 100 participants. Which researcher will have the largest margin of error given that all of the researchers had a standard error equal to 5?
A: Researcher C
B: All researchers will have the same margin of error
C: Researcher A
D: Researcher B
C: Researcher A
Which factors will influence the margin of error when the population standard deviation is unknown? Check all that apply.
A: The critical value
B: The sample standard deviation
C: The sample size
D: The standard error
A: The critical value
B: The sample standard deviation
C: The sample size
D: The standard error
A study of depression at UCLA recruits 100 participants. The result indicates a confidence interval of depression mean from 60 to 70. Which of the following is a correct interpretation of the 95% confidence interval?
A: We are 95% confident that the interval from 60 to 70 includes the sample mean of depression level
B: We are 95% confident that the range from 60 to 70 includes the population mean of depression level
C: If another study recruits another 100 participants, it is 95% likely that the new sample mean would fall between 60 to 70
B: We are 95% confident that the range from 60 to 70 includes the population mean of depression level
The critical value used for constructing a confidence interval for a sample is:
A: The uniform distribution
B: The t distribution
C: The normal distribution
D: It doesn’t matter what distribution you use
B: The t distribution
What t-distribution is more similar to a normal distribution?
A: One with a low number of degrees of freedom
B: One with a high number of degrees of freedom
B: One with a high number of degrees of freedom
A researcher is studying exam anxiety in college students. They collect data from N=400 students and calculate a sample mean of 4 and standard deviation of 2. Which of the following would be the correct way to calculate the 95% confidence interval? (CV = critical value)
A: 4 +/- (CV x 2 ÷ 400)
B: 4 +/- (CV x 2 ÷ √400)
C: CV +/- (4 x √400 ÷ 2)
B: 4 +/- (CV x 2 ÷ √400)
What do we mean when we say that we are 95% confident? Select all that apply.
A: If we draw many samples with the same size, then 5% of the confidence intervals computed from each sample will not include the true population mean
B: If we draw many samples with the same size, then 95% of those samples will yield confidence intervals that will include the true population mean
C: If we draw many samples with the same size, then 95% of those samples will yield the same confidence intervals
A: If we draw many samples with the same size, then 5% of the confidence intervals computed from each sample will not include the true population mean
B: If we draw many samples with the same size, then 95% of those samples will yield confidence intervals that will include the true population mean
