Chapter 12: Sampling Distribution of the Mean and Z-test Flashcards
Characteristics of Random Sampling (2)
- population chance of selection?
- members of the population chance of selection?
- Each possible sample of a given size has equal chance of being selected
- All members of the population have equal chance of being selected into the the sample.
Why is Random sampling important?(2)
- why is it required?
- what does it assure about the sample?
- required to apply laws of probability to a sample
- assures sample is representative of the population.
What is an experiment?
- tests influence of an IV on a DV
What are hypothesis?
- statement of prediction
What two kinds of hypothesis are there?
- Alternative hypothesis (Ha)
- Null Hypothesis (Ho)
What exactly is the Alternative Hypothesis?
- States there is a difference between the conditions due to the IV.
What exactly is the Null Hypothesis?
- the logical counterpart of Ha…mutually exclusive and exhaustive.
aka there is no difference between the conditions due to the IV.
What does it mean to be a Directional Hypothesis?
- specifies a direction of the effect from the IV.
ex: a new drug INCREASES an effect on mood.
What does it mean to be a Nondirectional hypothesis?
- specifies the IV has an effect, but no direction is stated..
ex: a new drug HAS an effect on mood.
If Ha is nondirectional than what does Ho state?
- IV has no effect
- ex: New drug HAS NO effect.
If Ha is directional that what does Ho state?
- IV has no effect or an effect in the opposite direction.
Ex:
Ha= new drug increases mood.
Ho= new drug has NO EFFECT on mood or makes it WORSE..
Results are always evaluated against what?
the null hypothesis
From the null hypothesis evaluation it is possible to calculate what?
- Now mathematics are available for the probability of what ?
- calculate probability of chance events
- no mathematics for the probability of Ha
What is the Alpha level used for? (3)
- calculate the probability of the obtained results if chance alone were operating
- if probability is < critical probability level, reject that Ho
- If reject the Ho, results are statistically significant.
What are the rules for interpreting alpha level?
- Obtained probability < alpha, reject Ho
Obtained probability > alpha, fail to reject Ho or retain Ho..
Sometimes , chance can be a troll….. hmm…what are the errors possible?
- Type 1 Error ; reject Ho when it is true…
- Type 2 Error: retain Ho when it is false….
Fill in the state of reality Table:
Decision |Ho is true | Ho is false
Retain Ho | (A) | (B)
Reject Ho | (C) | (D)
A) correct decision
B) Type 2 error
C) Type 1 error
D) correct decision
There is a relationship between alpha and what?
- Type 1 and 2 errors….
Alpha level usually set at a minimum of it =??
This limits the probability of making what error?
- 0.05
- type 1 error
Why not make the alpha more extreme like alpha= 0.01 ????
- the probability of making a type two error increases.
Sampling Distribution of a statistic:
- what values are included in this?
- What is the assumption made ?
- all the values that the statistic can take
- probability of getting each value under the assumption that it resulted from chance alone
What are the two steps to sampling distribution of a statistic?
- Calculate the appropriate statistic
- evaluating the statistic based on its sampling distribution
What is the Null-hypothesis population???
- Set of population scores that would result if the experiment were done on the entire population and the IV had no effect.
What is the sampling distribution of the mean?
- All the values the mean can take, along with the probability of getting each value if sampling is random from the null hypothesis population.
Explain the empirical approach: Population with μ and σ??
- Draw samples of a fixed size N ( whole population)
- calculate mean
- calculate probability of getting each mean if chance alone were operating
Characteristics of Sampling distribution of mean?
- distribution of sample means
- has a mean and standard deviation
- μx(bar)= mean of the sampling distribution of means
- σx(bar)= standard deviation of the sampling distribution of mean.
μx(bar) is equal to what?
what is the calculation for σx(bar) ?
- the μ of the original population
- σx(bar)= σ/ \/N (square root of N) also called the standard error of mean
The sampling distribution of the mean is ___ distributed. Depends on ___ of ____ population. Depends on the ___ size (__), which is usually set at around X>_…
- normally distributed
- shape, raw score population
- sample size (N)
- > 30
When faced with a problem that you need to calculate a Z score, you will be given what?
- mu of the population, standard deviation of the entire population
- Xobt of the sample and N of sample
What is Zcrit sued for?
- Z crit is the critical region of rejection of Ho
- this is determined by the Alpha level.
What is the rule for Rejecting Ho based on Z crit?
- If | zobt | > | zcrit |, reject Ho, if not we retain Ho
What is the formula for Zobt???
Zobt= Xobt- Ux/ σx
What is a critical region?
- all values of the statistic that allow rejection of Ho which is determined by alpha 0.05 and 0.01!
What are the two tests for alpha one can use to get Zcrit?
What significance does the sign of Zobt carry?
- 1-tail test = directional hypothesis (0.05 or 0.01)
- 2- tail test= non directional hypothesis ( if alpha = 0.05 than each end of the distribution will be 0.025)
- if 1 tail test, it determines which side Zcrit falls
- If 2 tail, it places it in one of the two critical regions
