Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Exam 2 Study Guide - Introductory Statistics | STAT 2000, Study notes of Statistics

University of Georgia (UGA)Statistics

Exam 2 Study Guide Material Type: Notes; Class: Introductory Statistics; Subject: Statistics; University: University of Georgia; Term: Fall 2011;

Typology: Study notes

2010/2011

Uploaded on 10/23/2011

meg6492
meg6492 🇺🇸

5

(1)

7 documents

1 / 10

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
STAT 2000
Franklin
Test 2 Study Guide
- Test 2 is scheduled for Tuesday, October 4 and Wednesday, October 5.
- Practice problems with answer are on eLC.
- Review sessions are Monday and Tuesday night, 6-8pm Fine Arts 300. Review
handout is on eLC.
Probability: a measure of how likely an event of interest will occur. It is a proportion of
times a particular outcome can occur, divided by the total number of possible outcome, so
probability is always between 0 and 1, inclusive (so we don’t count endpoints). Total
of all probabilities equals 1.
Outcome: a particular event of interest.
Law of Large Numbers: The more you repeat an experiment, the more likely you will get a
probability that is close to the actual probability of the event occurring.
Long run: large number of experiments
Short run: a small number of experiments
Two Types of Probability:
1.) Classical Probability – what we would expect in the long run, or….
Relative Frequency Probability – the observed proportion of successful events
-P(A) = number of ways an event can occur
-An outcome that has the same trait as the event of interest, we call that outcome a
“success”
-The probability of the event happening is the number of successes divided by the
number of possible outcomes.
2.) Subjective Probability – probability based on subjective/personal judgment.
How to find probabilities:
-List all possible outcomes.
- Sample space: the set of all possible outcomes of an experiment.
- Event: an subset of a sample space.
oTwo events are independent if the chances of one event occurring have no
impact on if the other event occurs.
oIf 2 events are not independent, they are dependent on each other.
Complement (Ac): the complement of event A is all outcomes in the sample space that are
not in event A.
Probability of Ac = 1 - Probability of A
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Exam 2 Study Guide - Introductory Statistics | STAT 2000 and more Study notes Statistics in PDF only on Docsity!

STAT 2000

Franklin

Test 2 Study Guide

  • Test 2 is scheduled for Tuesday, October 4 and Wednesday, October 5.
  • Practice problems with answer are on eLC.
  • Review sessions are Monday and Tuesday night, 6-8pm Fine Arts 300. Review handout is on eLC. Probability: a measure of how likely an event of interest will occur. It is a proportion of times a particular outcome can occur, divided by the total number of possible outcome, so probability is always between 0 and 1, inclusive (so we don’t count endpoints). Total of all probabilities equals 1. Outcome: a particular event of interest. Law of Large Numbers: The more you repeat an experiment, the more likely you will get a probability that is close to the actual probability of the event occurring. Long run: large number of experiments Short run: a small number of experiments Two Types of Probability: 1.) Classical Probability – what we would expect in the long run, or…. Relative Frequency Probability – the observed proportion of successful events - P(A) = number of ways an event can occur - An outcome that has the same trait as the event of interest, we call that outcome a “success” - The probability of the event happening is the number of successes divided by the number of possible outcomes. 2.) Subjective Probability – probability based on subjective/personal judgment. How to find probabilities: - List all possible outcomes. - Sample space: the set of all possible outcomes of an experiment. - Event: an subset of a sample space. o Two events are independent if the chances of one event occurring have no impact on if the other event occurs. o If 2 events are not independent, they are dependent on each other. Complement (Ac): the complement of event A is all outcomes in the sample space that are not in event A. Probability of Ac^ = 1 - Probability of A

If Probability of A was .62, the complement would be 1 - .62 =. AND Probabilities: Event A AND B occur at the same time; the probability of event A AND B consists of the outcomes that are in both A and B. OR Probabilities: At least A OR B occurs (or both), the probability of event A OR B consists of the outcomes that are in event A or B. If we are given a contingency table we can find the AND/OR probabilities easily. For a randomly selected person, what is the probability they are middle-aged and has low pressure? 64/219 =. What is the probability that a randomly selected person is old or has high blood pressure? 104 (total of old people)/ 219 + 124 (total with high blood pressure) /219 – 73 (old people with high blood pressure) */219 =. Note: you have to subtract 73/219 (old people with high blood pressure) because they were already counted in the first 2 proportions in the totals. Conditional Probability: The probability of A, given that B has already occurred. If you roll a die, and you know you rolled an even number, what is the probability you rolled a six? 1/3 = .3333 (there are 6 numbers on a die, 3 are even and 6 is one of these even numbers) We can use a contingency table to find conditional probabilities. Given that a battery selected is AA, what is the probability of it working? 700/760 =. What is the probability of randomly selecting a C battery? 700/1460 =.

We can also use the z-score to find this! It’s just as easy. Find the z-score = (65-50)/10 = 1. For the mean enter 0 and for the standard deviation enter 1. For Prob (x ??) select ≤ (because we want to know what the probability below 65) then enter 1.5 in the next box and hit calculate! Your answer is the same, .9332! *Always set the mean to 0 and the standard deviation to 1 when using the z-score to find a probability. How to find percentile using z-score: Ex) multiplied byample: find the z-score that is in the 90th^ percentile (meaning you scored higher than 90 percent of people)

  • Set mean to 0 and standard deviation to 0.
  • For Prob (x) multiplied by ??) select ≤ (because we want to know what the probability below 90% or .90)
  • Do not enter anything in the next bow because this is where your z-score will show up.
  • In the next box enter .90 and hit calculate!

Sampling Distribution 3 different distributions: Population Distribution:

  • the entire distribution from which we take the sample Sample (Data) Distribution:
  • the distribution of the sample data for a particular given sample.
  • The shape of the sample mirrors that population. Sampling Distribution: - the probability a sample statistic, such as a sample mean. - It is a distribution of all the possible values for the sample statistic. - The shape of it will be approximately normal under the conditions, which we will soon present. The Expected Mean of the Sampling Distribution of the Sample Mean: the mean of all possible sample means we could obtain in random sampling will be the same as the overall population. (also denoted with μ) Standard Deviation: - the standard deviation of a sampling distribution is called the standard error. (it’s just another type of standard deviation) - it measures the variability of a sample statistic like the sample mean. - Standard error = σ / √(n) (so important to know!) Shape: - One of the following has to be true to make sure the distribution is bell-shaped or approximately normal: o If the population is normally distributed, then the sampling distribution of the sample mean is normally distributed as well, regardless of sample size. o For a large sample, n ≥ 30, the sampling distribution of the sample mean is approximately normal, regardless of distribution of population. This is called the Central Limit Theorem. Ex) multiplied byample from HW question that I thought was really helpful to show this: Samples n = 16 are selected from a population with mean 80 and standard error 8. Mean = 80 (given) Standard deviation = 2 (8/√16) Shape = doesn’t say, can’t determine Sample n = 100 are selected from a population with mean 80 and standard error 8. Mean = 80 (given) Standard deviation = .80 (8/√100) Shape = approx) multiplied byimately normal (Central Limit Theorum, n >30)

Ex) multiplied byample: Suppose the test scores of Test 1 has a mean(μ) = 82 and standard deviation(σ) = 10. We took a sample of n = 25 students. If we took many samples of 25 students and found the sample mean, what would the standard deviation of these sample mean test scores be and what is it called?

- called the standard error - standard deviation of sample mean would = 10/√25 = 2 - the population is left skewed as well - what is the probability that the sample mean of test scores for a sample size n = 25 is higher than 83? =. o In StatCrunch set mean = 82 and st. dev. = 2 (because we want to know the probability of students in just the sample) and for Prob(X ??) select > because we want to know the probability that scored above 83) and enter 83 in the next box and hit calculate! Example from HW question: Average temperature in households in 67.6°F. Standard deviation is 4.2°F. A random sample of 51 households is selected. What is the probability that the average of this sample will be above 68.8°F? =.

  • First find the standard error because we are using the sample. 4.2/√51 =. - In StatCrunch set mean = 67.6 and st. dev. =. - Prob(X ??) select > because we want to know the probability above 68.8) and enter 68.8 in the next box and hit calculate!

What is the probability that the average of this sample will be within 1.4 degrees of the population mean? 67.6 + 1.4 = 69 67.6 – 1.4 = 66. (we want to find the probability between these 2 number)

- In StatCrunch set mean = 67.6 and st. dev. =. - Prob(X ??) select < because we want to know the probability below 69) and enter 69 in the next box and hit calculate! - We get. - Keep < the same and enter 66.2 in the next box - We get .00864 (subtract this number from .99135) - .99135 - .00864 =. What is the probability that the average of this sample will be within 1.4 standard errors of the population mean? - standard error = z-score - In StatCrunch set mean = 0 and st. dev. = 1 since we are using the z-score. - P (-1.4 ≤ z ≤ 1.4) - P (z ≤ -1.4) =. - P (z ≤ 1.4) =. - .9192 - .0808 =. Notation:

Would a sample proportion value of .60 be unusual? Yes, because we already know that almost all of the proportions are between .39 and .54. Notation: Overall Summary of both sampling distributions: *Remember to identify the problem as dealing with means or proportions before doing anything!