A confidence interval for mu is centered at the sample mean.
Correct Answer
True
True. The interval is x-bar minus the error bound to x-bar plus the error bound, so the sample mean sits exactly in the middle.
Category: Point Estimates
Question 2
With the same data, a 99% confidence interval is narrower than a 90% confidence interval.
Correct Answer
False
False. A higher confidence level uses a larger critical value, which makes the error bound larger, so the 99% interval is wider than the 90% interval.
Category: Width and Sample Size
Question 3
Every t-distribution is symmetric about zero.
Correct Answer
True
True. Like the standard normal curve, the t-distribution is bell-shaped and centered at zero, with matching left and right halves.
Category: Student's t-Distribution
Question 4
The confidence level of an interval is the probability that the method produces an interval that misses the parameter.
Correct Answer
False
False. That probability is alpha. The confidence level is its complement, the long-run proportion of intervals that do contain the parameter, and the two add to 1.
Category: Interpreting Confidence Intervals
Question 5
Increasing the sample size, with everything else unchanged, makes the error bound for a mean smaller.
Correct Answer
True
True. The error bound z x sigma / sqrt(n) has sqrt(n) in the denominator, so a larger sample gives a smaller error bound and a narrower interval.
Category: Width and Sample Size
Question 6
The plus-four method is used to build confidence intervals for a population mean.
Correct Answer
False
False. The plus-four method is an adjustment for a population proportion: it adds two successes and two failures before computing the interval.
Category: Plus-Four Method
Question 7
A confidence interval for a population proportion is built with z critical values rather than t critical values.
Correct Answer
True
True. The error bound for a proportion is z x sqrt(p'q' / n). The t-distribution is used for a mean when sigma is unknown, not for a proportion.
Category: Population Proportion
Question 8
When no estimate of p is available, using p' = 0.1 in the sample size formula gives the most conservative sample size.
Correct Answer
False
False. The product p'q' is largest, 0.25, when p' = 0.5, so p' = 0.5 gives the largest and therefore most conservative sample size.
Category: Width and Sample Size
Question 9
For a 95% confidence interval, the area beyond the critical value in each tail is 0.025.
Correct Answer
True
True. Alpha is 0.05 for 95% confidence, and it is split equally between the two tails, leaving 0.025 in each.
Category: Interpreting Confidence Intervals
Question 10
For the same confidence level, a t critical value with 5 degrees of freedom is smaller than the z critical value.
Correct Answer
False
False. Because the t-distribution has more area in its tails, its critical value is larger than z at the same confidence level, which makes t intervals wider.
Category: Student's t-Distribution
Question 11
Once a particular confidence interval has been computed, it either contains mu or it does not.
Correct Answer
True
True. Mu is a fixed number and the computed interval is fixed, so no probability remains for that one interval. The confidence level describes the method over many samples.
Category: Interpreting Confidence Intervals
Question 12
If a confidence interval for mu is (30, 40), the point estimate x-bar is 10.
Correct Answer
False
False. The point estimate is the center of the interval, (30 + 40) / 2 = 35. The value 10 is the width of the interval.
Category: Point Estimates
Question 13
To cut the error bound for a mean in half, with everything else unchanged, the sample size must be multiplied by 4.
Correct Answer
True
True. The error bound is proportional to 1 / sqrt(n), and multiplying n by 4 doubles sqrt(n), which halves the error bound.
Category: Width and Sample Size
Question 14
A t-distribution with 3 degrees of freedom is closer to the standard normal curve than one with 30 degrees of freedom.
Correct Answer
False
False. The t-distribution looks more like the standard normal as the degrees of freedom increase, so the one with 30 degrees of freedom is much closer.
Category: Student's t-Distribution
Question 15
The error bound for a mean is the distance from the sample mean to either endpoint of the interval.
Correct Answer
True
True. The interval extends one error bound below x-bar and one error bound above it, so the error bound is half of the total width.
Category: Error Bound
Question 16
A wider confidence interval gives a more precise estimate of the parameter.
Correct Answer
False
False. A wider interval covers a larger range of plausible values, so it is less precise. Narrower intervals give more precise estimates.
Category: Interpreting Confidence Intervals
Question 17
The t critical value depends on both the confidence level and the degrees of freedom.
Correct Answer
True
True. The shape of the t-distribution changes with the degrees of freedom, so the value that leaves alpha / 2 in each tail depends on both quantities.
Category: Student's t-Distribution
Question 18
A 95% confidence interval for mu of (12, 18) shows that 95% of the individuals in the population have values between 12 and 18.
Correct Answer
False
False. The interval estimates where the population mean lies. It says nothing direct about where individual values fall, and individual values are usually far more spread out than this.
Category: Interpreting Confidence Intervals
Question 19
In a confidence interval for a proportion, q' equals 1 - p'.
Correct Answer
True
True. The estimated proportion of failures q' is the complement of the estimated proportion of successes p', so the two always add to 1.
Category: Population Proportion
Question 20
A confidence interval for a population proportion is always centered at 0.5.
Correct Answer
False
False. The interval is centered at the sample proportion p', the observed share of successes. The value 0.5 is used only as a conservative guess when planning a sample size.
Category: Population Proportion