Hypothesis Testing flashcards, diagrams and study guides
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. The null hypothesis would say that class size has no effect on student learning.
2. False. A larger alpha means that the boundaries for the critical region move closer to the center of the distribution.
3. The .02 would be split between the two tails, with .01 in each tail. The z-score boundaries would be z = +2.33 and z = —2.33
A chart representing data that shows the frequency that a statistic occurs on a number line, usually represented with marks above the number line for every occurrence of a simulation or data point occurring.
Experimentally determine the outcome of a study, through manipulation of objects or using an online applet.
Represents the probability or the percentage likelihood of an event occurring through random chance.
b) consumers, evaluators, and creators of science
e) All of the above
100 research studies, 61 not replicable, 15% generated completely different results Message of study: research methods are not static, but dynamic.
the mean of the population is equal to 55 the population proportion is not less than .65
the mean of the population is greater than 55 the population proportion is less than .65
you don't reject a null hypothesis that is false
the probability of correctly rejecting a false H0 (null hypothesis e.g. there is no difference between 2 groups). In other words, the probability of detecting an effect that is really there.
Beta = the probability of making a type II error, i.e. incorrectly failing to reject H0, which asserts that there is no significant difference between the 2 groups.
Alpha = the probability of making a type 1 error, i.e. incorrectly failing to accept H0. Also known as false positive.
The probability that the study will produce a statistically significant result IF the research hypothesis is true *pay attention to IF, because if the research hypothesis is false, you DO NOT want to get significant results (that would be a type I error)
When a study has only a small chance of being significant even if the research hypothesis is true
Beta + Power = 100%, so power is opposite of beta Beta = 100% - Power since Beta is the probability of not getting a significant result when the research hypothesis is true
An inferential statistical method that uses the data from a sample to draw inferences about a population
The actual distance between a sample mean M and a population mean µ.
The average distance between a sample mean M and the population mean µ that would be expected if H0 was true.
Q: What is the probability if you pick a sample (say, of 4 people) at random from the population, that this sample's mean will be greater than 132? Before: p( x > 132 ) Now: p ( x̅ > 132 ) So, instead of the x guy, we're talking about the . . . x-men.
A: Instead of 1 person at a time, do 1 sample at a time. Sample 1 (4 students): x̅ = 110 Sample 2 (4 students): x̅ = 105 . . . . . . . . . .
A: Still bell-shaped and symmetric BUT . . . • Taller • Thinner Q: How much thinner? A: If the x distribution's sd were σ, then x̅. EX: σ/√N *NOTE: The new graph is called the "sampling distribution of means" (see pg. 170). p( x̅ > 132) = .003% OLD: z = x - μ / σ σ = 16, μ = 100, N = 4 *NEW: z = x̅ - μ / σ/√N Steps: 1) Draw picture 2) x → z 3) go to z table for %
Which of the following accurately describes a hypothese test?
What is MEASURED by the DENOMINATOR of the z-score test statistic?
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis (H1) say about the treatment?
a process that uses sample statistics to test a claim about the value of a population parameter
a statement about a population parameter
a statistical hypothesis that contains a statement of equality *≤, =, ≥ Ho
a statistical method that uses sample data to evaluate a hypothesis about a population
1) State hypothesis 2) Set the criteria for a decision 3) Collect data and compute sample stats 4) Make a decision - compare sample data with the hypothesis prediction - If the sample mean is consistent the hypothesis was reasonable - If the sample mean is not consistent then conclude that the hypothesis was wrong.
to decide between two explanations: 1) the difference between the sample and the population can be explained by sampling error (there does not appear to be a treatment effect). 2)the difference between the sample and the population is too large to be explained by sampling error (there does appear to be a treatment effect)
-Ho is what historically it is (null hypothesis) -Ha is what we think it is (<,>,not=)
-The probability of observing a test statistic as extreme as, or more extreme than, the statistic obtained from a sample, under the assumption that the null hypothesis is true. -The smaller the p-value is the stronger the evidence against Ho provided by the data.
- if p-value is as small, or smaller than α (alpha) the data is statistically significant at level -"not likely to happen by chance"
(H0) is the foundational assumption about a population and represents the status quo. It is a statement of equality (==).
(Ha) is a different assumption about a population and is a statement of inequality (<<, >>, or ≠≠). Using a hypothesis test, we determine whether it is more likely that the null hypothesis or the alternative hypothesis is true.
is the probability of getting a test statistic at least as extreme as the one you got, assuming H0H0 is true. A PP-value is calculated by finding the area under the normal distribution curve that is more extreme (farther away from the mean) than the z-score. The alternative hypothesis tells us whether we look at both tails or only one.