Intro to Stats - Exam 3 and Final Exam

1. Define the field of Statistics
The science of collecting, analyzing, and interpreting data.

2. Define population.
The overall group about which you have interest.

3. Define sample.
A subset of the population.

4. Define random sample.
A sample where all members of the population have the same chance of being included.

5. Define representative sample.
A sample that has makeup consistent with the population.

6. Define parameter and statistic.
A parameter is a numerical characteristic of a population, and a statistic is a numerical characteristic of a random sample.

7. What is the whole point of statistical inference?
To draw conclusions about a population based upon a sample (or about a parameter based on a statistic). Also, to see what statistics tell us about parameters (or samples tell us about populations). (Any one of these answers would be correct.)

8. In words, what is a standard deviation? (I’m not looking for the formula.)
On the average, how much a list of data deviates from the mean.

9. What does a z-score tell you? (I’m not looking for the formula.)
How many standard deviations above the mean a raw score is.

10. If I say that the raw score 75 is at the 60th percentile, what does that mean?
Sixty percent of the data falls below 75.

11. What is probability?
A measurement of the likelihood of the occurrence of some chance event.

12. Define outcome.
A possible result of a probability experiment.

13. Define sample space.
A collection of all possible outcomes.

14. Define event.
A subset of the sample space, or a collection of outcomes. (Either answer is correct.)

15. Define simple event.
An event that consists of exactly one outcome.

16. Between what values do probabilities fall?
0 and 1

17. Define a random variable.
A function that turns outcomes into numbers.

18. Define a pdf (probability distribution function)
A function that shows how the probabilities are distributed over the different values of a random variable.

19. What is a sampling distribution?
A pdf for a statistic.

20. What is an unbiased estimator?
A statistic is called unbiased for a parameter if the value we expect that statistic to give is the parameter.
or
The mean of the statistic's sampling distribution is the parameter.

21. Suppose I tell you that the interval of numbers from 77 to 83 is a 95% confidence interval for the mean µ of a population. Briefly explain what is meant by that confidence interval. (Correct version.)
We are 95% sure that the interval [77, 83] surrounds the parameter µ.

22. Suppose I tell you that the interval of numbers from 77 to 83 is a 95% confidence interval for the mean µ of a population. Briefly explain what is meant by that confidence interval. (Incorrect/layman's version.)
We are 95% sure that the parameter µ falls into the interval [77, 83] .

23. What is an alpha value (or significance level) for a hypothesis test?
The probability of a type I error.
or
The probability of rejecting H0 when H0 is true.

24. One way to perform a hypothesis test leads us to something called a p-value. What is a p-value?
The probability of getting data as extreme as you actually got, assuming the null hypothesis is true.
or
The probability of making a mistake by rejecting H0.

25. What does a correlation coefficient tell you about the data points on a scatterplot?
How tightly the data points fit to a line.

26. Between what values do correlation coefficients fall?
-1 and 1

27. What is a line of regression (or best-fitting line), and what is it used for?
It is the line on a scatterplot that the data fits best to, and it is used for predicting y-values based upon x-values.

28. What is ANOVA? (For Final Exam only)
Analysis of Variance: a method of testing the equality of several means by looking at the variance of the data.