PY211 exam 2

what are the cutoff z-score of one-tailed tests at the 5% level?

+-1.64

what are the cutoff z-score of two-tailed tests at the 5% level?

+-1.96

A team of researcher predict that showing a certain film will change people's attitudes toward alcohol. The researchers then randomly select 36 people, show them the film, and give them an attitude questionnaire. The mean score on the attitude test for these 36 people is 70. The score for people in general on this test is 75, with a standard deviation of 12. Using the five steps of hypothesis testing and the 5% significance level, carry out a Z test to see if viewing the film changes people's attitudes toward alcohol. What is/are the cutoff sample score(s)?

+1.96 -1.96

statistical power

- the probability that the study will produce a statistically significant result is the research hypothesis is true.

The criterion or level of significance in behavioral research is typically set at what probability value (x)?

.05, .01

Name steps of hypothesis testing

1) Restate the question as a research hypothesis and a null hypothesis about the populations 2) Determine the characteristics of the comparison distribution 3) Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected 4) Determine your sample's score on the comparison distribution 5) Decide whether to reject null hypothesis

A team of researcher predict that showing a certain film will change people's attitudes toward alcohol. The researchers then randomly select 36 people, show them the film, and give them an attitude questionnaire. The mean score on the attitude test for these 36 people is 70. The score for people in general on this test is 75, with a standard deviation of 12. Using the five steps of hypothesis testing and the 5% significance level, carry out a Z test to see if viewing the film changes people's attitudes toward alcohol. What is the sample's Z score? Decide whether to reject the null hypothesis:

70-75/2=-2.5 is -2.5 more extreme than -1.96? YES so reject

Define 0.05 significance level

A 0.05 significance level is the cutoff on the comparison distribution with a probability of​ 5% that a score will be at least that extreme if the null hypothesis were true. This probability is usually written as p < 0.05.

if what is measured/percieved is true and reality is true:

Correct

As sample size (N) increases, the standard error of the mean

DECREASES

Step 5 of Hypothesis Testing

Decide whether to reject null hypothesis -compare your actual sample's z-scores (step 4) to the cutt off z-score (step 3) -

using a more extreme significance level _____power

Decrease

Step 3 in Hypothesis Testing

Determine cut off sample score on the Comparison Distribution at which the null hypothesis should be rejected -ideally set a target against what they will compare your results -they decide in advance that IF the result of their study is a athlete performing +2 SD above the mean, they will REJECT the null -use cutoff score on comparison distribution with a probability of 5% that a score will be at least that extreme if the null hypothesis is true -researchers REJECT null if probability os sample score this extreme i=(if null=true) is less than 5%

Step 2 of Hypothesis Testing

Determine the characteristics of the comparison distribution -you compare the actual sample's score to this comparison distribution

Step 4 of Hypothesis Testing

Determine your sample's score on the comparison distribution -carry out experiment and get the results for sample -compute z-scores for the sample's raw score based on the pop. mean and SD of comparison distrubition

ex) Studying how a new studying method will affect academic performance. The new method could hurt performance because students are having to learn new method. Or, it could increase performance by teaching them new skills. What is the research hypothesis? Null hypothesis?

Ha: new studying method changes the level of academic performance research hypoth: M1 does not equal M2 null hypoth: M1=M2

Step 1 of Hypothesis Testing

Restate the question as a research hypothesis and a nulll hypothesis about the populations -state research hypothesis -state null hypothesis

how to protect against type 1 error

Setting α to be low (i.e. p < .001) can lessen the chance of a Type 1 Error, but it can lead to a Type 2 error...

Under what conditions is it reasonable to assume that a distribution of means will follow a normal​ curve?

The distribution of means will follow a normal curve when the distribution of the population of individuals follows a normal​ curve, or when each sample is of 30 or more individuals.

protect against type 2 error

To protect against Type 2 error, you can set a more lenient significance level (i.e. p < .1). But this can lead to Type 1 error.

A team of researchers predict that showing a certain film will change people's attitudes toward alcohol. The researchers then randomly select 36 people, show them the film, and give them an attitude questionnaire. The mean score on the attitude test for these 36 people is 70. The score for people in general on this test is 75, with a standard deviation of 12. Using the five steps of hypothesis testing and the 5% significance level, carry out a Z test to see if viewing the film changes people's attitudes toward alcohol. What is the variance of the distribution of means?

Two tailed solve for variance of distribution of means 12^2/36= 144/36=4

type 2 error also called?

Type 2 error is also called beta (ß)

what is a distribution of means?

a a distribution of means of samples of a given size from a population

research hypothesis

a prediction about the difference btw populations ex) pop 1 athletes will on avg perform better than pop 2 M1>M2

what is a hypothesis?

a prediction intended to be tested in a research study (an IF, THEN, BECAUSE statement)

The mean of the distribution of means is _________ the mean of the original population of individuals

about the same as

The shape of the distribution of means is ___________.

approximately normal

bigger effect size, _______ power

bigger

smaller SD , _______ effect size

bigger

two tailed test

considering possibility that the sample cul be

if what is measured/perceived is false and reality is false:

correct

if we accept null hypothesis (H0) and null hypothesis (H0) is true:

correct decision

if we reject null hypothesis (H0) and Ha is true:

correct decision

Which of the following is not a step in hypothesis testing? a) state the hypothesis b) set the criteria for a decision c) compute the test statistic d) determine your theory

d) determine your theory

larger population, SD _____power

decreases

How does the following affect the power of a planned study? A larger population standard deviation ____________ power & using a more extreme significance level (for example, 0.01 instead of 0.05) _____________ power.

decreases, decreases

A team of researcher predict that showing a certain film will change people's attitudes toward alcohol. The researchers then randomly select 36 people, show them the film, and give them an attitude questionnaire. The mean score on the attitude test for these 36 people is 70. The score for people in general on this test is 75, with a standard deviation of 12. Using the five steps of hypothesis testing and the 5% significance level, carry out a Z test to see if viewing the film changes people's attitudes toward alcohol. What is the standard deviation of the distribution of means?

find variance of distrib. and square root. =2

bigger mean difference, _______power

greater

cut-off sample score (aka. critical value)

how extreme of a sample score would it have to be for it to be unlikely that they could get such an extreme score if the null hypothesis were true -probability of 5% (p<.05)

effect size

is a measure of the difference between population means.

A distribution of means will be _______ than the distribution of individuals from which the samples were taken

less spread out

The spread of the distribution of means is ___________ the spread of the distribution of the population of individuals

less than

In a planned study, there is a know population with a normal distribution, μ = 0, and σ = 20. What is the predicted effect size if the researchers predict that those given an experimental treatment have a mean of 10?

medium solve for effect size: d=(10-0)/20=.5

The decision in hypothesis testing is to retain or reject which hypothesis: the null or alternative hypothesis?

null hypothesis

directional hypothesis

predicting a particular direction of differences btw populations ex) predicting pop1 has a higher mean than pop 2 ie) suppose the research hypothesis is that gettin $10 million will make a person happier than gen. population. -null hypoth: money will either have no effect or make a person less happy * if research hypothesis is M1>M2 then null hypothesis is M1<M2

A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-statistic of z = -2.60. Assuming that the researcher is using a two-tailed test, what is the correct statistical decision (Hint: use Table)?

reject the null hypothesis with either α= .05 or α=.01 use z-table to find .05 in % in tail column. should be 2.57 or 2.58 Compare z-score to alpha values/is it more extreme?

two-tailed test (non-directional hypothesis)

research hypothesis states that an experimental procedure will have an effect, without saying it will produce a very high/low score

decision errors

situations in which the right procedures lead to the wrong decisions ex) deciding that the null hypothesis is false when its true

The variance of the population of individuals is 400 and there are 25 individuals in each sample. What is the standard error of the mean?

solve for variance of distribution of means, square root it. 400/25=16 square root of 16=4

if asked to find standard error, what are you trying to find?

the SD of the distribution of means

A researcher computes a one-sample z-test in two studies. Both studies used the same alpha level, placed the rejection region in both tails, and measured the same sample mean. The researcher selects a sample of 30 participants in Study 1 and decides to retain the null hypothesis. She selects a sample of 60 participants in Study 2 and decides to reject the null hypothesis. Which of the following is the best explanation for why the decision was different in Study 1 and Study 2?

the different decisions in Study 1 and Study 2 are possible because the second test was associated with greater power to detect an effect

null hypothesis

the lack of difference btw populations ex) there is no difference in the performance of athletes btw pop 1 and pop 2 ie) athletic performance is not influenced by whether athletes take the specially purified supplement M1=M2

What term is used to identify the standard deviation of the distribution of means?

the standard error of the mean (SE or SEM) -if asked to find standard error know you are trying to fin

one tailed test

the test of a directional hypothesis -can be a test in either direction (positive or negative)

Setting the significance level cut-off at .05 means that you will make a __________ error 5% of the time. The significance level (the chance of making this error) is called _________.

type 1 alpha (α).

if what is measured/percieved is true but reality is false;

type 1 (false positive)

If we reject null hypothesis (H0) but null hypothesis (H0) is true:

type 1 error

if we accept null hypothesis (H0) but Ha is true:

type 2 error

if what is measured/perceived is false and reality is true:

type 2 error (false negative)

finding percentages based on alpha?

use table to find .05 or .01 in %in tail column.

comparison distribution

what we use to make inferences from the data of our study/experiment -used to determine how well the distribution can be approx. by the normal distribution ex) The comparison distribution in muscle supplement example is the distribution for Population 2, since this population represents the athletic performance if the null hypothesis is true.

If the null hypothesis is rejected, then did we reach significance?

yes

In a two-tailed test, what do you do to the significance percentage

you have to divide the significance percentage between the two tails. ex) with a 5% significance level, you reject a null hypothesis only if the sample is so extreme that either the top 2.5% or the bottom 2.5% of the comparison distribution. (keeps overall level of significance at a total of 5%)

Several students took a standardized test to get into graduate school. The mean score for these students was 1000 and the standard deviation was 200. Arya made a score or 1200. What would her z-score be?

z= 1200-200/1200 = +1

A population of scores has µ = 44. My sample has a mean of 40 which corresponds to z = -1.00. What is the standard deviation of the distribution of means?

z=M-µM/SD know that µM=µ so -1 = 40-44/SD -1=-10/SD 4=SD