Stats test 2

What is the formula for Natural Variation?

"natural variation" of x¯ is within 3 σ/√n of mean

When you spin a 1961 penny, the probability that it will stop with the head side up is 0.1. What is the mean of the sampling distribution of pˆ for 150 spins of a 1961 penny? (a) 0.1 (b) 0.9 (c) 1.5 (d) 15

(a) 0.1

Who are the subjects in the Salk vaccine experiment? (a) 400,000 children who participated in the study (b) 200,000 children who received the vaccine (c) second-grade American children (d) all American children

(a) 400,000 children who participated in the study

When you spin a 1961 penny, the probability that it will stop with the head side up is 0.1. Are we safe in using the normal distribution to calculate the probability that pˆ is .075 or less for 150 spins of a 1961 penny? (a) Yes (b) No

(a) Yes

What is the factor in the Salk vaccine experiment? (a) type of inoculation (b) vaccine (c) placebo (d) polio status

(a) type of inoculation

Students applying for the music program are randomly assigned to 2 of the 4 possible audition times: Monday at 4:00, Monday at 5:00, Tuesday at 7:00, Tuesday at 8:00. What is the probability that both of a student's audition times will be on the same day? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3 (e) 4/3

(b) 1/3

Jennie scored 600 on the SAT Mathematics exam. Her friend Gerald took the American College Testing (ACT) test and scored 21 on the math part. ACT scores are normally distributed with mean 18 and standard deviation 6. SAT scores are also normally distributed with mean 500 and standard deviation 100. Assuming that both tests measure the same kind of ability, who has the higher score? (a) Gerald (b) Jennie (c) Gerald's and Jennie's scores are the same (d) Cannot be computed with information given

(b) Jennie

Recall: Birth weights of full-term babies are normally distributed with µ = 3485 g and σ = 425 g. Baby Emma was full term. Her birth weight was 4350 g. What was her standardized weight (z)? (a) z = 1.25 (b) z = 2.04 (c) z = 2.46 (d) z = 3.59

(b) z = 2.04

Consider flipping 2 coins and then counting the number of heads. What are the possible outcomes for this experiment? (a) 1, 2 (b) 0, 1 (c) 0, 1, 2 (d) 1, 2, 3

(c) 0, 1, 2

An automobile salesman tells you that he gets a bonus if you report on a post-sale survey that he was effective and courteous. What kind of bias might be present in this survey? (a) nonresponse (b) undercoverage (c) misleading response (d) no bias

(c) misleading response

What is the response variable in the Salk vaccine experiment? (a) type of inoculation (b) polio, vaccine (c) polio status (d) vaccine, placebo

(c) polio status

Birth weights of full-term babies are approximately normally distributed with µ = 3485 g and σ = 425 g. Approximately what proportion of full-term babies weigh more than 3060 grams? (a) 16% (b) 34% (c) 68% (d) 84%

(d) 84%

In a famous study, 5200 patients were categorized into 2 groups according to their soda habit. After 4-years of follow-up, the rate of heart disease was higher in the "regularly drank" group than the "sparingly drank" group. What kind of study is this? (a) historical comparison experiment (b) unreplicated experiment (c) confounded experiment (d) observational study

(d) observational study

A public opinion poll in Ohio wants to determine whether or not registered voters in the state approve of a measure to ban smoking in all public areas. They randomly select fifty registered voters from each county in the state and ask whether they approve or disapprove of the measure. What type of sampling design is this? (a) convenience sampling (b) cluster sampling (c) simple random sampling (d) stratified random sampling (e) multistage random sampling

(d) stratified random sampling

What are the treatments in the Salk vaccine experiment? (a) syringe, school nurse (b) polio, vaccine (c) polio status (d) vaccine, placebo

(d) vaccine, placebo

Do cars get better gas mileage with clean air filters? Gas mileage for 10 cars with dirty air filters and clean air filters was studied. Each car was tested once with a clean air filter and once with a dirty air filter (with the order of the testing randomized). What type of study is this? (a) an observational study based on a simple random sample (b) an observational study based on a stratified random sample (c) an observational study based on a multistage random sample (d) a randomized controlled experiment (e) a matched pairs experiment

(e) a matched pairs experiment

What are the principles of Data Ethics?

- safety and well-being of the subjects must be protected • all individuals must give their informed consent before data are collected • individual data must be kept confidential

What are three common bad ways to sample populations?

1. Convenience 2. Volunteer Response 3. Quota

What are common bad ways of drawing cause-effect conclusions?

1. Historical Comparison Experiments (No controls) 2. Unreplicated Experiments 3. Confounded Experiments (different conditions in experiment)

What are signs of unnatural variation?

1. One point above the upper control limit or below the lower control limit 2. Run of 9 points in a row on same side of the centerline (as unlikely as one point outside the control limits) As soon as an "out-of-control" signal is observed, STOP the process and look for a cause

Define Theoretical Probability

1. Theoretical (or classical) probability - determined by logic and the properties of the game/experiment • Example: P("roll a 2") = 1/6

What are the 4 different types of probability sampling?

1. simple random sampling 2. cluster sampling 3. stratified random sampling 4. multistage sampling

What is cluster sampling

1. used when population is naturally divided into groups called clusters. (e.g., households are divided into city blocks) 2. each cluster is essentially representative of the population as a whole 3. a random sample of clusters is taken 4. all individuals in the selected clusters are included in the sample

What are the percentage of areas in the distribution intervals?

34, 13.5, 2.35, .15

Event:

A collection of possible outcomes Example: We can write the event "rolling an odd number on a die" as the set {1, 3, 5}

Define Randomized Block Design (RBD)

A group of individuals that are: • similar with respect to some characteristic known before the experiment begins, and that characteristic is expected to affect the response to the treatments. • often equal in number to the number of treatments. What is a randomized block design? An experimental design where the random assignment of individuals to treatments is carried out separately within each block.

Discrete or continuous random variable? 1. Blood pressure a. discrete b. continuous 2. Body temperature (◦F) a. discrete b. continuous 3. Area code for phone a. discrete b. continuous 4. # of coins in pocket a. discrete b. continuous

B,B,A,A

Describe the center, spread, and shape of Xbar ;

Center: mean of sampling distribution of x bar = µ Spread: standard deviation of sampling distribution of x bar = sigma/sqrt(n) Shape: Case 1: Population normal. The shape of the distribution of x¯ is normal · Case 2: Population non-normal. The shape of the distribution of x¯ is approximately normal when n is large (n ≥ 30) CLT

Define Control, Confounding

Control: an effort to reduce effects of lurking variables Confounding: situation in which effects of lurking variables cannot be distinguished from effects of factors

Define Statistic

Corresponding numerical fact in the sample (e.g., pˆ=sample proportion)

Define Experimental Study

Definition: a study design where treatments are imposed on individuals before observing response Purpose: determine if treatments cause change in response

Define Diagnostic Bias

Diagnosis of subjects biased by preconceived notions about effectiveness of treatment • preconception is confounded lurking variable Solution: Perform studies in which both subjects and diagnosticians are blinded called double blinded

Dieting Example Matched Pairs

Dieting with exercise and dieting without exercise is compared using twenty sets of identical twins • Explanatory Variable: whether dieting includes exercise • Response Variable: cholesterol level • Block: a pair of identical twins • Comparison: two treatments • Randomization: randomly select one twin to diet with exercise; the other to diet without • Replication: 20 pairs of identical twins

What is mew and sigma for x bar?

Distribution of ¯x for all possible SRSs of size n from a population with mean µ and SD σ

Define Empirical Probability

Empirical (or observational or long-run) probability - approximated by playing the game (running the experiment) many times and observing frequency of occurrence • Example: P("instructor makes a 15-foot shot with basketball") ≈ 0.65, because she made 13 out of 20 • Empirical probabilities are approximate, but theoretical probabilities are often impossible to calculate; e.g., P("randomly choosing a student that is male, a stat major, and from California")

What is quota sampling?

Force the sample to meet specified quotas • e.g., recruit 200 females and 300 males between 45 and 60 • participants within a subgroup are not selected randomly, rather by convenience or some sort of judgment call

What is the Central Limit Theory?

If you take a large SRS of size n from any population, then the shape of the sampling distribution of x¯ is approximately normal • shape gets more normal as n increases • n ≥ 30 is considered large • CLT allows us to use the standard normal table to compute approximate probabilities associated with x

Random Phenomenon:

Individual outcome unpredictable, but outcomes from large number of repetitions follow regular pattern

What is Volunteer response sampling?

Individuals select themselves • television polls • online polls • ratemyprofessor.com

Define Inteviewer Effect

Interviewer influences responses Examples: • rude • intimidating to some people • subtle clues or gestures

Define the Law of Large Numbers

Law of Large Numbers: As the number of trials (or repetitions) of the experiment/game increases, the relative frequency of the event gets closer and closer to the theoretical probability of the event

How do you calculate standard deviations for all

Mew + or - sigma

For normal ditribution what is mean, and standard deviation?

Mew= the mean Sigma= standard deviation

Define Parameter

Numerical fact about the population (e.g., p=population proportion)

Define question order

Order of questions promotes certain responses Examples: • happiness question precedes debt question • and vice-versa

What is the formula for P hat?

P hat= #of individuals in category of interest/# of individuals in sample

Define Hawthorne Effect

Phenomenon where people in an experiment behave differently from how they would normally behave; attention/observation bias. (demand characteristics)

What are the principles of Valid Experiments?

Principles of Valid Experiments 1. Control/Comparison 2. Randomization 3. Replication 4. Double-Blinding

What is stratified random sampling

Quota sampling done right! 1. classify population into groups (strata) that are different from each other (e.g., classify according to age or gender) 2. individuals within a group (stratum) share a similar characteristic (e.g., all are males or all are children) 3. select SRS from every group 4. combine SRS's

Define Response Variable, Lurking Variable

Response Variable: characteristic measured on each subject Lurking Variables: variables that affect response variable, but not planned factors

Define Placebo Effect

Response by human subjects due to the psychological effect of being treated. • psychological effect is confounded lurking variable Consequence: ineffective treatment appears effective relative to untreated subjects Solution: Include placebo in control

What is simple random sampling?

Sample of specified size chosen such that every possible set of that size has equal chance of being the sample 1. put all names in hat, 2. stir well, 3. draw out desired number of names

What is Convenience sampling?

Select individuals in easiest possible way • first spuds off truck • stop people in Wilk at noon • Psych 101 class • first 25 chickens caught

Define Misleading response

Selected individuals lie or give inaccurate answer (sensitive issues) Examples: • Did you wash your hands? • Have you cheated? • What is your income, age? • Are you a voter?

Define Non-response

Selected individuals refuse to answer or can't be contacted Examples: • hang-ups • on vacation • refusal to mail census forms

Sample Space:

Set of all possible outcomes

Define Undercoverage

Some individuals have no possibility of being selected Examples: • homeless • phoneless

Define Subject, Factor, and Treatment

Subject: individual to which treatment applied Factor: planned explanatory variable Treatment: experimental condition applied to subject = value of factor

Define Randomized Controlled Experiment (RCE)

Subjects assigned to treatments such that each subject has an equal chance of being assigned to any possible treatment (typically with the same number of subjects per treatment) Recipe: • put all names in a hat, • stir well, • draw out desired number of names for treatment A, etc.

Characteristics of Normal Distributions

Symetric, Mean=Median, Bell curved, one peak

Define Sampling Distribution of p hat

The distribution of the values of the sample proportions (pˆ) in repeated samples is called the sampling distribution of p hat The sampling distribution of a sample statistic refers to what the distribution of the statistic would look like if we chose a large number of samples from the same population.

Probability of an Outcome:

The proportion of times that an outcome occurs in many, many repetitions (plays) of the random phenomenon.

Define Xbar

The sampling distribution of a sample mean is a theoretical probability distribution It describes the distribution of: • all sample MEANS • from all possible random samples • of the same size • taken from the same population

Define p hat

The sampling distribution of a sample proportion is a theoretical probability distribution It describes the distribution of: • all sample PORPORTIONS • from all possible random samples • of the same size • taken from a population

True or False: A z-score measures how many standard deviations an individual value is from the mean.

True

How many types of random variables are there?

Two types of discrete random variable: • Discrete categorical (e.g., college major) • Discrete quantitative (e.g., persons living in household)

Define Question Wording

Wording of question leads, misleads, or confuses Examples: • loaded words • double negatives • wordy questions

For the the Sampling Distribution of pˆ, shape?

approximately normal if n is large, but large depends on how close p is to 0.5. Guideline: np ≥ 10 and n(1 − p) ≥ 10

Define Replication

assign enough subjects (> 1!) to treatments to be able to detect important effects

Define Random Variable:

characteristic that is measured on each individual; e.g., cost, height, yield, gender

Define Control/Comparison

control lurking variables by including comparison treatments, using homogeneous subjects; used to measure placebo effect

For the the Sampling Distribution of pˆ, what is the mean?

mean is p

Define Double Blinding

neither the subjects nor the people who evaluate them know which treatment each subject is receiving; used to prevent experimenter effect

Define Randomization

neutralize effects of lurking variables by assigning subjects to treatments randomly

Define Lack of Realism

realism is often compromised by controlled study conditions, choice of homogeneous subjects, application of treatments. SolutionSolution: 1. awareness of hidden bias 2. admit limitations of experiments

For the the Sampling Distribution of pˆ, what is the Spread?

standard deviation of sampling distribution of pˆ is sqrt((p(1−p))/n)

What is multistage sampling

take sample at each level: e.g., 1. SRS of states 2. for selected states, SRS's of counties 3. for selected counties, SRS's of people 4. combine SRS's of people

Define Continuous Random Variable:

variable that can take on any value in an interval so that all possible values cannot be listed; e.g., time, height, temperature

Define Discrete Random Variable:

variable whose possible values are a list of distinct values; e.g., gender, opinion, # of arrests, shoe size

What is the formula for z score with statistics/parameters?

z= P hat-p/sqrt((p(1-p)/n))

Why do we care about Sampling Distribution?

• Sampling distributions allows us to assess uncertainty of sample results • If we knew the spread of the sampling distribution, we would know how far our x¯ might be from the true µ (one way or another) • If a sampling distribution has a lot of variability, then if you took another sample it's likely you would get a very different result • About 95% of the time the sample mean will be within 2 sigma/sqrt(n)of the population mean • This tells us how "close" the sample statistic should be to the population parameter

Define Matched Pairs

• Special case of randomized block designs • Block: Pair of individuals or pair of measurements • Explanatory variable: two treatments • Examples: • Twins: each receiving a treatment • Two treatments on each individual • Measurements before and after treatment on each individual

What are the probability rules?

• a probability must be a number between 0 and 1 • the sum of probabilities from all possible outcomes must equal 1 • if two events cannot occur simultaneously, the probability either one or the other occurs equals the sum of their probabilities • the probability that an event does not occur equals 1 minus the probability that the event does occur

Define Noncompliance

• failure to submit to the assigned treatment • refusal to follow the protocol of the experiment Consequence: invalid results

mathematical conversion of normally distributed variable to standard normal variable

• if x is normally distributed with mean µ and standard deviation σ, then z = (x − µ)/σ

Define open/closed questions

• open questions are less restrictive, but responses are more difficult to summarize • closed questions may be biased by the options provided • closed questions should permit options such as "Other " and/or "Not Sure" if those options apply

What are potential flaws in Randomized Controlled Experiment?

• placebo effect • diagnostic bias • lack of realism • Hawthorne effect • noncompliance

Define Probability distribution:

• set of possible outcomes in sample space AND the probability (or %) associated with each outcome • e.g., all presidential candidates considered by Salt Lake County residents • probabilities must sum to 1 • can be represented by a table, formula, or graph

Define Observational Study

• subjects choose which treatment to receive or naturally belong to one of the treatment groups • lurking variables that influence choice confounded with treatments • passive data collection: observing, measuring, counting, subjects are undisturbed • media often improperly attribute cause-effect conclusions to these

Even if you sample well, probability samples may still have bias due to:

• undercoverage • non-response • misleading response • interviewer effect • question order • question wording