Exploring Data
Sampling&Experiment
Probability &variables
confidence interval
significant test
100
What is the term for the middle value of a sorted dataset?
The median
100
What is the name for a sample where every individual in the population has an equal chance of being selected?
A simple random sample (SRS).
100
If two events are mutually exclusive, what is the probability that both occur at the same time?
0 (they cannot occur together).
100
What is the purpose of a confidence interval in statistics?
To estimate an unknown population parameter with a range of plausible values, at a specified confidence level.
100
What is the null hypothesis (H_0) in a significance test?
A statement of "no effect" or "no difference," which we assume true unless evidence suggests otherwise
200
A distribution with a long tail to the right is called_____.
Right-skewed (positively skewed).
200
What is the term for a study where neither the subjects nor the researchers know who is in the treatment or control group?
A double-blind study.
200
What is the formula for the expected value (mean) of a discrete random variable?
200
For a confidence interval for a proportion, what conditions must be met to use the normal approximation?
np \geq 10 and n(1-p) \geq 10 (success-failure condition).
200
What does the p-value represent in a hypothesis test?
The probability of observing a test statistic as extreme or more extreme than the one calculated, assuming the null hypothesis is true.
300
What does the standard deviation measure about a dataset?
The spread/variability of data around the mean.
300
A treatment group that receives no active treatment, to compare against the real treatment, is called a ______.
Control group (placebo group).
300
A binomial distribution requires which two key conditions for its trials?
Fixed number of independent trials, each with two outcomes (success/failure) and constant probability of success.
300
If we increase the confidence level (e.g., from 90% to 95%), what happens to the width of the confidence interval?
It becomes wider (to be more confident we capture the true parameter).
300
If the p-value is less than the significance level (\alpha), what decision do we make about the null hypothesis?
We reject the null hypothesis.
400
For a normal distribution, approximately what percentage of data lies within 1 standard deviation of the mean?
68% (the empirical rule).
400
What is the main difference between an observational study and an experiment?
Experiments impose treatments on subjects to observe responses; observational studies only observe existing conditions.
400
If X and Y are independent random variables, what is the variance of their sum Var(X+Y)?
Var(X) + Var(Y) (variances add for independent variables).
400
When constructing a confidence interval for a mean, when do we use a t-distribution instead of a z-distribution?
When the population standard deviation (\sigma) is unknown.
400
What is a Type I error in hypothesis testing?
Rejecting the null hypothesis when it is actually true (false positive).
500
If you transform data by adding a constant to every value, which measures of spread change?
None (range, IQR, standard deviation remain unchanged).
500
What is the name of the bias that occurs when people choose to respond to a survey, leading to an unrepresentative sample?
Voluntary response bias.
500
What type of distribution models the number of successes in a fixed interval of time/space, given a constant average rate?
Poisson distribution.
500
A 95% confidence interval for a population mean is (12, 18). What is the margin of error?
3 (the distance from the center 15 to either bound).
500
For a two-sample t-test comparing means, what does the alternative hypothesis H_a: \mu_1 - \mu_2 \neq 0 represent?
That there is a difference between the two population means (not equal to zero).