This is a data set with mean 5, median 5, mode 6, and range 9.
What is (for example), 1, 3, 4, 4, 6, 6, 6, 10
100
The distribution of the sample mean Xbar from a sample of size n from a population with mean mu and variance s^2.
What is -- a trick question! If the population is normally distributed, then the distribution of Xbar is N(mu, s^2/n). If n is large, then the distribution is approximately this.
100
These are the two type of estimators we have learned. One is a value, and one is a range of values.
What are point estimates and interval estimates?
100
True or False: This is the correct interpretation of a 95% confidence interval of (4.5, 6.7) for the mean mu of a distribution: "The mean mu will be between 4.5 and 6.7 with probability .95."
What is FALSE! The mean mu is fixed, not random, so it makes no sense to talk about its probability. The interval itself is random! (See the other questions in this category)
100
What is the intuition behind why an MVUE is a good estimator for an unknown parameter?
What is, the MVUE is the unbiased estimator with the smallest variance. We clearly want an unbiased estimator so that on average the estimator will give the correct parameter. We also would prefer the estimator to have small variance so that more often than not, it is close to the true parameter.
200
The three quartiles of the data set 23, 17, 30, 19, 26.
What are 18, 26, and 28?
200
The sum of the square of n-1 standard normal random variables has this distribution, as does (n-1)S^2/sig^2 when S^2 is a sample variance from n-1 observations of a population with variance sig^2.
What is chi-square with n-1 degrees of freedom? (See Theorems 4.2.7 and 4.2.8 in the text, and also our class notes.)
200
This is the intuition behind why the method of moments yields a reasonable point estimate for an unknown parameter(s).
What is: The sample should be fairly representative of the population. Thus, the sample moments should be close to the true moments. Since the true moments depend on the unknown parameter(s), we can approximate the true moments by the sample moments and solve for the unknown parameters.
200
This is the correct interpretation of a 95% confidence interval of (4.5, 6.7) for the mean mu of a distribution.
What is: We are 95% confident that the true mean mu lies between 4.5 and 6.7. This means that if we repeatedly took samples and created such intervals that 95% of the time our interval created from the sample will contain the true mean mu.
200
This is the 95% confidence interval for the true proportion of defective items from a sample of 60 which showed 20 defective items?
What is (using the normal approximation), (.21, .45). [See Example 6.2.4]
300
The components of a boxplot.
What are, the median (center line), first and third quartiles (outer edges of box), smallest and largest values (end of whiskers)
300
The ratio of two independent chi-square random variables has this distribution, as does the ratio of two sample variances.
What is the F-distribution?
300
This is the method of moments estimator for p, when p is the unknown probability of a coin landing hands, and you observe n coin flips.
What is Xbar, the proportion of heads observed in the n flips (see the Bernoulli question from Quiz 2).
300
This is a pivotal quantity for an unknown parameter t.
What is a function of t whose distribution does not depend on t?
300
This is the MLE for p from a geometric distribution, after observing a sample X1, X2, ..., Xn of size n.
What is 1/Xbar? (See Example 5.3.2 in the text)
400
This is the 97th percentile of test scores if they are normally distributed with average 1100 and standard deviation 300.
What is 1664?
400
When the population variance is unknown, we may approximate it by the sample variance S, in which case (Xbar - mu)/(S/sqrt(n)) has this distribution which looks like the normal distribution especially for large n.
What is student t-distribution?
400
This is the intuition behind the MLE as a good estimate for an unknown parameter.
What is: We compute how likely it is to observe the sample that we have observed, and choose the parameter that maximizes this liklihood.
400
What is the intuition behind approximating confidence intervals for large sample sizes?
What is that by the Central Limit Theorem, for large sample sizes, many quantities become approximately normally distributed. Thus in these cases, we can use the confidence interval for a normal distribution.
400
Compute the bias of the estimator Xbar (the sample mean) for the parameter b of an exponential distribution with pdf
f(x) = (1/b)exp(-x/b) for x>0.
What is 0? Since E(Xbar) = mu = b.
500
The differences between a bar graph and a histogram.
What are spaces between the bars (only in bar graphs), bar graphs are for qualititative data, histograms are for quantitative data.
500
We can approximate a binomial random variable by a normal random variable because of *this theorem* and using *this* type of correction.
What is the Central Limit Theorem and the continuity correction?
500
This is how to show that an estimator T for an unknown parameter t is unbiased.
What is, you need to show that E(T) = t. Recall that the bias of T is E(T) - t, which will be zero if T is unbiased.
500
What happens to the margin of error in a confidence interval as the sample size n goes to infinity?
What is it goes to zero?[Can you prove this for a normally distributed population? Hint: What happens to the standard error?]
500
A good pivotal quantity for a uniform distribution on (a,b) is this when a is known.
What is (bhat - a)/(b-a) where bhat is the MLE of b (equal to the largest value of the sample)