STATISTICS TRIVIAL PURSUIT (SORT OF) FOR REVIEW (MATH 17)

COLORS AND CATEGORIES

Blue – Basic Graphs and Descriptive Statistics Pink – Assumptions (cumulative) Yellow – Statistical Theory and History Brown – Interpretations Green – Last 1/3 Inference Orange – Other Hypothesis Testing Related

BLUE 1

What are the descriptive statistics that are sensitive to outliers?

BLUE 2

Provide the name and primary purpose of this graph.

BLUE 3 Provide a basic description of the distribution of this variable

from its graph (remember there are 3 things to describe).

BLUE 4

What are the descriptive statistics used in the creation of a boxplot?

BLUE 5

Name the rule used to compute outliers, and describe how to apply it.

BLUE 6

Name graphs that are appropriate to display categorical variables, and state whether or not you should discuss the shape of distributions based on those graphs.

BLUE 7

Compare/contrast these 2 distributions based on the plot.

BLUE 8

A standard deviation of a measurement in feet is 3.4 feet, from a sample with a mean of 29.2. Interpret the standard deviation.

BLUE 9

This plot is part of the preliminary analysis for ….

BLUE 10

If there was a high outlier in the distribution of a particular variable, and it was removed, what descriptive statistics are likely (or certain) to change to a significant extent?

PINK 1

What is the assumption that all chi-square tests have in common?

PINK 2

What is the assumption related to sample sizes for a 2 sample z-test?

PINK 3

What is the assumption related to sample size when constructing a confidence interval for p?

PINK 4

What are the specifics of the nearly normal condition for a paired t-test?

PINK 5

What are the specifics of the nearly normal condition for ANOVA?

PINK 6

What are the specifics of the 2 assumptions in regression related to error terms?

PINK 7

You are told that the randomization and independence condition is met for a sample of high school students who were asked how much money they received for their most recent birthday. Describe what the randomization and independence assumption means in this context.

PINK 8

What are some example tests where assumptions related to normality are NOT required?

PINK 9

What are the specifics of the nearly normal condition for a 2-sample t-test?

PINK 10

What is the assumption that all tests/CIs have in common but which (since it is common to all) Prof. Wagaman doesn’t require that you write down when you list assumptions?

YELLOW 1

What is a sampling distribution for a statistic? (conceptually)

YELLOW 2

(Fill in at least 3 of the blanks for credit)The t distribution was discovered by

___________ who published under the pseudonym ____________. He discovered the t distribution while working for _____________ in Ireland. Specifically he was working in the field of ______________ (2 words, but one blank) and was primarily responsible for checking out _________, one of their many products.

YELLOW 3

What does the Central Limit Theorem say?

YELLOW 4

How are z-scores computed, and what are they useful for? (variety of answers)

YELLOW 5

When sampling distributions have standard deviations that involve unknown parameters, and we plug in estimates for those parameters, we obtain what value(s)?

YELLOW 6

Suppose 2 random variables X and Y are independent. X has mean 6 and standard deviation 3. Y has mean 14 and standard deviation 4.

What are the values of the mean and standard deviation of X+Y?

YELLOW 7

What are the differences between a chi-square test of homogeneity and a chi-square test of independence?

YELLOW 8

What are the three types of bias in sampling?

YELLOW 9

If you are designing an experiment and you have 3 different drugs you want to try, and you want to try them at 2 different doses each (1 pill or 2 pills daily), and you want to include (a) placebo group(s), how many treatments are there in your experiment?

YELLOW 10

Name and describe two different sampling techniques.

BROWN 1

Running a hypothesis test for slope equal to 0 or not, you obtain a t-test statistic value of -2.14. Interpret this test statistic.

BROWN 2

A linear regression results in an R-squared value of .81. Assuming linear regression was appropriate, interpret this R-square in terms of general X and Y variables.

BROWN 3

A random sample of n=16 observations yields an s=24 (sample standard deviation). What is the numerical value of the standard error of the sample mean? Also, interpret this value.

BROWN 4

Describe what is wrong with the statement: “A p-value is the probability that the null

hypothesis is true.”

BROWN 5

A 95% confidence interval for a mean weight of a new dog breed goes from (25.2, 34.6) pounds. Interpret the confidence interval given here.

BROWN 6

A regression results in an s_e value of 3.46. The y-axis goes from 36 to 109. What does the s_e value represent, and what does it tell you about how well the regression does?

BROWN 7

A p-value for an ANOVA testing for equality of 5 means with an F of 24.56 is .0359. Interpret this p-value.

BROWN 8

A 95% confidence interval for a mean weight of a new dog breed goes from (25.2, 34.6) pounds. Interpret the confidence level used here.

BROWN 9

A conclusion in a t-test of mu=150 vs. mu>150 is given as:

Our evidence is not inconsistent with our null hypothesis.

How should this conclusion be changed to be correct?

BROWN 10

A p-value for a two-sided two sample z-test is .1470 based on a Z of 1.45. Interpret this p-value.

GREEN 1 Which set(s) of graphs indicate it would NOT

be appropriate to perform an ANOVA? Explain.

GREEN 2

You want to know if the distribution of class year among Reunion workers is equally split among first-years, sophomores, and juniors. What test is appropriate?

(Note, I am assuming that seniors can’t get hired to work Reunion, if they can, change this to equally split among all four class years).

GREEN 3

An ANOVA where the null hypothesis is rejected results in multiple comparisons of:

Estimate lwr upr2-1 4.146737 -2.737867 11.0313423-1 -3.742933 -10.627537 3.1416713-2 -7.889670 -14.774274 -1.005066

Summarize what this multiple comparisons shows you.

GREEN 4

If you wanted to know whether or not there is a significant association between heart rate and weight in rats, what statistical procedure would you perform?

GREEN 5

You want to compare the means of 4 groups. Describe why you would want to do an ANOVA rather than 6 t-tests to compare all pairs of means.

GREEN 6

You want to know if there is an association between t-shirt size (S,M,L,etc.) and class year at Amherst. What is the appropriate statistical procedure to perform?

GREEN 7

You want to know if a higher proportion of underclassmen have corrective lenses compared to upperclassmen. Explain why there is no appropriate chi-square test for this situation. What analysis could you run?

GREEN 8

A balanced ANOVA is an ANOVA where….

GREEN 9

Describe the similarities and differences in finding p-values for ANOVA and chi-square.

GREEN 10

A scatterplot for regression is given as:

R also reports an R-squared value of .81

What is the correlation between X and Y?

ORANGE 1

What is power and how would you increase it for a hypothesis test?

ORANGE 2

What is a Type I error?

ORANGE 3

If given a significance level of .035, for what p-values would you reject the null hypothesis?

ORANGE 4

Explain the difference between practically significant results and statistically significant results.

ORANGE 5

Most of the tests we learned in class were ______________ tests. If certain assumptions related to them are not met, you can run ________________ tests, one example of which is ________________________.

(Fill-in at least 1 blank).

ORANGE 6

Hypothesis tests and confidence intervals are based on an understanding of the __________________ _______________________ (two words) of statistics.

ORANGE 7

You are performing a t-test for mu=60 versus a 2-sided alternative and all conditions are satisfied. What is the expected value of your test statistic under the null hypothesis?

ORANGE 8

You are testing for p=.4 vs. p>.4 and all conditions are satisfied. Your sample results in 30 yes replies out of 100 responses. What can you say about your p-value for this test?

ORANGE 9

In order to use a confidence interval to do a one-sided t-test with a significance level of .05, what confidence level would need to be used?

ORANGE 10

You are testing for mu=50 vs. mu>50, and the appropriate confidence interval is (52,64). Can you reject your null hypothesis? Explain.

Final Exam is Monday, May 9th, 9 am -12 noon in SM 207

You can bring a two-sided page of notes and calculator, plus pen/pencils.

Office Hours: Thursday – 2-4 Friday – 1-4 Sunday – 2-4 pm, SM 206 or 207

Good luck studying!

REMINDER:

Math dept. end of semester picnic is Saturday from 12-2 at the Alumni House

THANKS FOR A GREAT SEMESTER!