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

Question 1

Characteristics of Random Sampling (2)

• population chance of selection?
• members of the population chance of selection?

Answer 1

• 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.

Question 2

Why is Random sampling important?(2)

• why is it required?
• what does it assure about the sample?

Answer 2

• required to apply laws of probability to a sample

- assures sample is representative of the population.

Question 3

What is an experiment?

Answer 3

• tests influence of an IV on a DV

Question 4

What are hypothesis?

Answer 4

• statement of prediction

Question 5

What two kinds of hypothesis are there?

Answer 5

• Alternative hypothesis (Ha)

- Null Hypothesis (Ho)

Question 6

What exactly is the Alternative Hypothesis?

Answer 6

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

Question 7

What exactly is the Null Hypothesis?

Answer 7

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

Question 8

What does it mean to be a Directional Hypothesis?

Answer 8

• specifies a direction of the effect from the IV.

ex: a new drug INCREASES an effect on mood.

Question 9

What does it mean to be a Nondirectional hypothesis?

Answer 9

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

Question 10

If Ha is nondirectional than what does Ho state?

Answer 10

• IV has no effect

- ex: New drug HAS NO effect.

Question 11

If Ha is directional that what does Ho state?

Answer 11

• 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..

Question 12

Results are always evaluated against what?

Answer 12

the null hypothesis

Question 13

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

Answer 13

• calculate probability of chance events

- no mathematics for the probability of Ha

Question 14

What is the Alpha level used for? (3)

Answer 14

• 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.

Question 15

What are the rules for interpreting alpha level?

Answer 15

• Obtained probability < alpha, reject Ho

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

Question 16

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

Answer 16

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

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

Question 17

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

Answer 17

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

Question 18

There is a relationship between alpha and what?

Answer 18

• Type 1 and 2 errors….

Question 19

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

This limits the probability of making what error?

Answer 19

• 0.05

- type 1 error

Question 20

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

Answer 20

• the probability of making a type two error increases.

Question 21

Sampling Distribution of a statistic:

• what values are included in this?
• What is the assumption made ?

Answer 21

• all the values that the statistic can take

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

Question 22

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

Answer 22

• Calculate the appropriate statistic

- evaluating the statistic based on its sampling distribution

Question 23

What is the Null-hypothesis population???

Answer 23

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

Question 24

What is the sampling distribution of the mean?

Answer 24

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

Question 25

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

Answer 25

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

Question 26

Characteristics of Sampling distribution of mean?

Answer 26

- 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.

Question 27

μx(bar) is equal to what? | what is the calculation for σx(bar) ?

Answer 27

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

Question 28

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

Answer 28

- normally distributed - shape, raw score population - sample size (N) - >30

Question 29

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

Answer 29

- mu of the population, standard deviation of the entire population - Xobt of the sample and N of sample

Question 30

What is Zcrit sued for?

Answer 30

- Z crit is the critical region of rejection of Ho | - this is determined by the Alpha level.

Question 31

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

Answer 31

- If | zobt | > | zcrit |, reject Ho, if not we retain Ho

Question 32

What is the formula for Zobt???

Answer 32

Zobt= Xobt- Ux/ σx

Question 33

What is a critical region?

Answer 33

- all values of the statistic that allow rejection of Ho which is determined by alpha 0.05 and 0.01!

Question 34

What are the two tests for alpha one can use to get Zcrit? | What significance does the sign of Zobt carry?

Answer 34

- 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