Variables and Sampling Methods
Class rank is what type of variable?
Categorical Ordinal
If a data set has values of 1, 3, 5, 6, 7, 11, what is the median?
5.5
A data set has a minimum of 42 and a maximum of 89. What is the range?
47
β₁ (beta-1) stands for...
the slope
What is the difference between a statistic and a parameter?
A statistic summarizes data from a sample, where a parameter summarizes data for a population.
Is the number of students in a STAT 206 class discrete or continuous?
Discrete
This measure is the value that occurs most often in a data set.
the mode.
This measure of variation is found by squaring each deviation from the mean and averaging those squared deviations.
Variance
A regression line is ŷ = 12.5 + 3.2x, where x is hours studied and y is exam score. Interpret the slope.
For each additional hour studied, the predicted exam score increases by 3.2 points, on average.
Exam scores are approximately normal with a mean of 76 and a standard deviation of 5. About what percent of scores fall between 66 and 86?
95%
A researcher numbers every student and uses a random-number generator to select 50 students. What sampling method is this?
Simple random sampling
Find the mean of: 4, 7, 9, 10, 15.
9
This measure of variation is the square root of variance and is expressed in the same units as the data.
Standard Deviation
For the model ŷ = 40 + 5x, a student who studied 6 hours actually scored 66. Find the residual.
66 − [40 + 5(6)] = 66 − 70 = −4
By Chebyshev’s Theorem, at least what percent of observations lie within 2.5 standard deviations of the mean?
84%
A researcher divides students into freshmen, sophomores, juniors, and seniors, then randomly selects students from each group. What sampling method is this?
Stratified sampling
Find the geometric mean of 2, 8, and 32.
8
Find the coefficient of variation for a data set with mean 40 and standard deviation 6.
15%
A regression analysis gives r = −0.76. What percentage of variation in y is explained by its linear relationship with x?
r² = (−0.76)² = 0.5776, so 57.76%
A data set has Q1 = 12 and Q3 = 26. Is a value of 48 a potential outlier?
Yes
A survey estimates that 62% of students prefer online homework, but the true percentage for all students is 58%. What is this difference called?
Sampling Error
In a right-skewed distribution, which measure is usually larger: the mean or the median?
The mean, because the extreme outliers pull it to the right.
A student’s z-score on an exam was 1.8. If the exam mean was 72 and the standard deviation was 10, what was the student’s original score?
90
A regression line predicting final-exam score from hours studied is:
ŷ = 58 + 4.5x
A student studied for 7 hours and scored 82. What is the residual, and does the model overpredict or underpredict the student’s score?
The model overpredicts the score by 7.5 points.
A normal distribution has a mean of 50 and a standard deviation of 8. What score marks the cutoff for the highest 2.5% of values?
66