Describing Data
What is the difference between mean and median?
The mean is the average of the data, while the median is the middle value when the data is ordered.
What is the probability of flipping heads on a fair coin?
.5
What is a simple random sample?
A sample where every individual and every group of individuals has an equal chance of being selected.
What is a confidence interval used for?
To estimate a population parameter using sample data.
What is the null hypothesis?
A statement of no effect or no difference, which we test against.
Name two ways to describe the spread of a distribution.
Range, standard deviation, IQR, or variance
What does it mean if two events are independent?
The occurrence of one event does not affect the probability of the other.
Name one source of bias in survey sampling.
Voluntary response, undercoverage, or nonresponse.
What does a 95% confidence level mean?
If we took many samples, about 95% of the confidence intervals would contain the true population parameter.
What does a p-value tell you?
The probability of observing the data (or more extreme) assuming the null hypothesis is true.
What shape does a histogram have if it is skewed left?
The tail is longer on the left and the bulk of data is on the right.
What’s the formula for conditional probability?
P(A|B) = P(A and B) / P(B)
What’s the difference between stratified and cluster sampling?
Stratified samples divide the population into groups and randomly sample from each group. Cluster samples randomly choose whole groups and sample everyone in them.
What two components make up a confidence interval?
Point estimate +or- margin of error.
What does it mean to reject the null hypothesis?
The data provides enough evidence to conclude the null hypothesis is unlikely to be true.
How do outliers affect the mean and standard deviation?
Outliers can significantly increase or decrease the mean and increase the standard deviation.
Explain the difference between mutually exclusive and independent events.
Mutually exclusive events cannot happen at the same time. Independent events do not affect each other’s probabilities.
Why is voluntary response sampling often unreliable?
It attracts people with strong opinions, which may not represent the population.
How does increasing the sample size affect the width of a confidence interval?
It makes the interval narrower.
What’s the difference between a Type I and Type II error?
rejecting a true null. Type II: failing to reject a false null.
Describe how to create a boxplot and interpret the five-number summary.
Find the minimum, Q1, median, Q3, and maximum. Plot these on a number line to form the box and whiskers. It shows the spread and center of the data.
A bag has 3 red, 2 blue, and 5 green marbles. What is the probability of pulling 2 red marbles in a row without replacement?
1/15
Describe how you would design a study to estimate how many students at your school eat breakfast.
Take a simple random sample of students, create a short survey asking if they eat breakfast, and calculate the proportion that say yes.
A 95% confidence interval for a population mean is (8.1, 9.7). What does this mean in context?
We are 95% confident that the true mean lies between 8.1 and 9.7.
In a test of significance, what factors affect the power of a test?
Sample size, significance level (alpha), effect size, and variability.