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Statistics > Chapter 12: Sampling Distribution of the Mean and Z-test > Flashcards

Chapter 12: Sampling Distribution of the Mean and Z-test Flashcards

1
Q

Characteristics of Random Sampling (2)

  • population chance of selection?
  • members of the population chance of selection?
A
  • 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.
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2
Q

Why is Random sampling important?(2)

  • why is it required?
  • what does it assure about the sample?
A
  • required to apply laws of probability to a sample

- assures sample is representative of the population.

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3
Q

What is an experiment?

A
  • tests influence of an IV on a DV
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4
Q

What are hypothesis?

A
  • statement of prediction
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5
Q

What two kinds of hypothesis are there?

A
  • Alternative hypothesis (Ha)

- Null Hypothesis (Ho)

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6
Q

What exactly is the Alternative Hypothesis?

A
  • States there is a difference between the conditions due to the IV.
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7
Q

What exactly is the Null Hypothesis?

A
  • the logical counterpart of Ha…mutually exclusive and exhaustive.
    aka there is no difference between the conditions due to the IV.
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8
Q

What does it mean to be a Directional Hypothesis?

A
  • specifies a direction of the effect from the IV.

ex: a new drug INCREASES an effect on mood.

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9
Q

What does it mean to be a Nondirectional hypothesis?

A
  • specifies the IV has an effect, but no direction is stated..
    ex: a new drug HAS an effect on mood.
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10
Q

If Ha is nondirectional than what does Ho state?

A
  • IV has no effect

- ex: New drug HAS NO effect.

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11
Q

If Ha is directional that what does Ho state?

A
  • 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..
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12
Q

Results are always evaluated against what?

A

the null hypothesis

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13
Q

From the null hypothesis evaluation it is possible to calculate what?
- Now mathematics are available for the probability of what ?

A
  • calculate probability of chance events

- no mathematics for the probability of Ha

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14
Q

What is the Alpha level used for? (3)

A
  • 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.
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15
Q

What are the rules for interpreting alpha level?

A
  • Obtained probability < alpha, reject Ho

Obtained probability > alpha, fail to reject Ho or retain Ho..

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16
Q

Sometimes , chance can be a troll….. hmm…what are the errors possible?

A
  • Type 1 Error ; reject Ho when it is true…

- Type 2 Error: retain Ho when it is false….

17
Q

Fill in the state of reality Table:
Decision |Ho is true | Ho is false
Retain Ho | (A) | (B)
Reject Ho | (C) | (D)

A

A) correct decision
B) Type 2 error
C) Type 1 error
D) correct decision

18
Q

There is a relationship between alpha and what?

A
  • Type 1 and 2 errors….
19
Q

Alpha level usually set at a minimum of it =??

This limits the probability of making what error?

A
  • 0.05

- type 1 error

20
Q

Why not make the alpha more extreme like alpha= 0.01 ????

A
  • the probability of making a type two error increases.
21
Q

Sampling Distribution of a statistic:

  • what values are included in this?
  • What is the assumption made ?
A
  • all the values that the statistic can take

- probability of getting each value under the assumption that it resulted from chance alone

22
Q

What are the two steps to sampling distribution of a statistic?

A
  • Calculate the appropriate statistic

- evaluating the statistic based on its sampling distribution

23
Q

What is the Null-hypothesis population???

A
  • Set of population scores that would result if the experiment were done on the entire population and the IV had no effect.
24
Q

What is the sampling distribution of the mean?

A
  • All the values the mean can take, along with the probability of getting each value if sampling is random from the null hypothesis population.
25
Q

Explain the empirical approach: Population with μ and σ??

A
  • Draw samples of a fixed size N ( whole population)
  • calculate mean
  • calculate probability of getting each mean if chance alone were operating
26
Q

Characteristics of Sampling distribution of mean?

A
  • 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.
27
Q

μx(bar) is equal to what?

what is the calculation for σx(bar) ?

A
  • the μ of the original population

- σx(bar)= σ/ \/N (square root of N) also called the standard error of mean

28
Q

The sampling distribution of the mean is ___ distributed. Depends on ___ of ____ population. Depends on the ___ size (__), which is usually set at around X>_…

A
  • normally distributed
  • shape, raw score population
  • sample size (N)
  • > 30
29
Q

When faced with a problem that you need to calculate a Z score, you will be given what?

A
  • mu of the population, standard deviation of the entire population
  • Xobt of the sample and N of sample
30
Q

What is Zcrit sued for?

A
  • Z crit is the critical region of rejection of Ho

- this is determined by the Alpha level.

31
Q

What is the rule for Rejecting Ho based on Z crit?

A
  • If | zobt | > | zcrit |, reject Ho, if not we retain Ho
32
Q

What is the formula for Zobt???

A

Zobt= Xobt- Ux/ σx

33
Q

What is a critical region?

A
  • all values of the statistic that allow rejection of Ho which is determined by alpha 0.05 and 0.01!
34
Q

What are the two tests for alpha one can use to get Zcrit?

What significance does the sign of Zobt carry?

A
  • 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

Statistics (21 decks)

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