statistics trivial pursuit (sort of)for review (math 17)

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!