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Data Analysis exam 2 > Chapter 6 > Flashcards

Chapter 6 Flashcards

1
Q

As sample size __, shape of distribution become more like __ curve.

A

increases,

normal

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2
Q

Larger samples show more clear n__ c__ and d__.

A

Normal Curves,

Distributions

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3
Q

Examples of normally distributed variables:

  • h__
  • w__
  • i_
  • r__ t__

N__( c__) variables CAN’T be normally distributed.

A 
height
weight
IQ
reaction time 
nominal (categorical)
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4
Q

Normal Curve:
Specific b__-shaped curve that is u__, s__, and defined m__.
-Describes the distributions of m__ variables.

-As the size of a s__ approaches the size of the p__, the distribution resembles a normal curve (as long as the population is n__ d__).

A

bell-shaped, unimodal, symmetric, mathematically.

many

sample, population
normally distributed

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5
Q

Standardization: allows for fair c__ when variables are on different s__.

  • comparing z-scores: number of s__ d__ a score is from the m__.
  • z distribution: n__ distribution of s__ scores.
A

comparisons, scales
standard deviations, mean
normal, standardized

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6
Q

A z score is the number of s__ d__ a particular score is from the m__.

A z score is part of its own distribution, the _ distribution, just as a raw score, such as a person’s height, is part of its own distribution, a distribution of heights.

A

standard deviations, mean

z

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7
Q

Most DV’s are assumed to be __ distributed.

A

normally

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8
Q

If a variable is normally distributed, we can know stuff about l__ of o__.

A

likelihood, occurence

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9
Q

Most stats are based on a__ of n__.

A

assumption, normality

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10
Q

In the Z distribution, the mean is _ and the standard deviation is _.

A

0, 1

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11
Q

Linear Transformations:
-when you add a constant to each score (e.g: x+4)
what happens to the mean?
what happens to the SD?

-when you subtract a constant from each score (e.g: x-6)
what happens to the mean?
what happens to the SD?

-when you divide each score by a constant (e.g. 2)
what happens to the mean?
what happens to the SD?

A

increases by 4
stays the same

decreases by 6
stays the same

decreases by 1/2
gets smaller by 1/2

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12
Q

What is μ

A

Population Mean (i.e. 0 for z distribution)

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13
Q

What is σ

A

Standard deviation (i.e. 1 for z distribution)

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14
Q

To convert RAW scores into their Z scores steps:

  • subtract the mean of the __ from the r__ score.
  • divide by the s__ d__ of the population.

Practice writing out the equation

A

population, raw
standard deviation

z= x-μ/σ

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15
Q

ex converting raw score into z score:

mean: 6.07
SD: 1.62
raw score: 5

Find the z score.

A

z= 5-6.07/1.62 = -0.66

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16
Q

To convert Z scores into their RAW scores steps:

  • multiply the _ score by the _ _ of the population.
  • add the __ of the population

Practice writing out the equation

A

z, SD
mean

x=z∗σ+μ

17
Q

ex converting z score into raw score:

mean: 6.07
SD: 1.62
z score: 1.81

A

x=1.81∗1.62+6.07 = 9.00

18
Q

If we can standardize raw scores on 2 different scales, by converting both scores to z scores, we can then __ the scores directly.

A

compare

19
Q

Ex of standardizing two raw scores on different scales:

-Lab A: measured reaction time after 1 drink of alcohol, the population mean was 2.1 seconds, with an SD of 0.3. Larry’s reaction time was 1.4 seconds.

-Lab B: measured reaction times after 2 drinks of alcohol. The population mean was 3.1 seconds, with an SD of 0.6.
Bill’s reaction time was 1.5 seconds.

When using a standardized scale, who has the larger (slower) reaction time?

A

Larry:

1.4-2.1/0.3 = -2.33

Bill:

1.5-3.1/0.6= -2.67

Larry has the larger Z score and slower time.
-Larry’s score is less negative so LARGER TIME. (larger is longer with time)

20
Q

Transforming Z scores into PERCENTILES:

  • z scores tell you __ a values fits into a __ distribution.
  • based on a normal distribution, there are rules about where scores with a _ value will fall, and how it will relate to a p__ rank.
  • use a__ under normal curve to calculate percentiles for any score.
A

where, normal

z, percentile

area

21
Q

Break down of percentiles associated with each standard deviation:

DRAW OUT

A

between 0 and 1/-1—> 34% each side

between 0 and 2/-2—> 14% each side

between 0 and 3/-3—> 2% each side

22
Q

Practice percentile problems:

1) -What percentage falls within 1 standard deviation of the mean?
2) -What percentage falls within 2 standard deviations of the mean?
3) -What percentage is less than the mean?
4) -If you have a raw score equal to z= -1, what is your percentile score?
5) -What is your percentile if z= +1
6) -What is your percentile if z=1.5
7) -What is your percentile if z=0.25
8) -What is your percentile if z= -2.5

A

1) 34% + 34% = 68%
2) 14+14+34+34=96 OR 100-4=96
3) 50%
4) 16th percentile because you add the percent from -1 and below.
5) 84th percentile
6) 91st percentile
7) 58.5th percentile
8) 1st percentile

23
Q

Practice percentile problems continued:

1) If the pop. has a mean of 125 and std deviation of 10, if you are at the 16th percentile, what would your score be?
2) If your score is 135, what is your percentile?

A

1) x = -1(10) + 125 = 115
so z = -1
(or just look at chart and where 16% is)

2) z = (135-125)/10 = 1, 84th percentile

24
Q

Check your learning problems:

Check Your Learning

•If the population mean score on a quiz is 10 and the standard deviation is 2:

1) •If a student’s score is 8, what is z?
2) •If a student’s z score is 1.4, what is the raw score?

A

1) z= -1

2) x=1.4 * 2 +10
=12.8

25
Q

The Central Limit Theorem:
-Distribution of s__ means is n__ distributed even when the p__ from which it was drawn is not n__.

  • A distribution of m__ is less variable then a distribution of i__ scores.
  • Variability c__.
A

Sample, normally
population, normal

means, individual

changes

26
Q

The mean of the d__ tends to be the mean of the p__.

mean=μ

A

distribution, population

27
Q

Standard deviation of the d__ tends to be __ than the standard deviation of the p__ of scores.

A

distribution, less

population

28
Q

What is :

M

N

A

M=sample mean

N=number of elements in the sample

29
Q

Standard error formula:

SD * Population Mean= SD/square root of number of elements in sample

The standard error is the standard deviation of the p__ divided by the square root of the sample s__, __. The formula is.

Write out in notation.

A

population
size, N

σ(M)=σ/√ N

30
Q

Standard Error: s__ d__ of the distribution of m__.

-S__ than SD; takes on smaller value as _ increases.

A

standard deviation, means.

smaller, N (number of elements in sample)

31
Q

Write out the Z statistic

A

z=(M-μ*M)/σM

aka z=(sample mean-population mean)/
standard deviation * sample mean

32
Q

The mathematical magic of large samples:

-Distribution of m__ follows c__ l__ theorem.

The shape of distribution approximates n__ curve IF:

  • p__ of scores has n__ shape OR
  • size of each s__ of distribution is n=__+
A

means, central limit

normal
population, normal
sample, 30+

33
Q

Example calculating the z statistic using population data:

A pizza delivery chain claims that it delivers its pizzas to any location within a 15 mile radius within an average of 30 minutes, with a standard deviation of 12 minutes. Suppose a researcher employed by a competitor orders 16 pizzas to be delivered to different locations with a 15 mile radius, and computes a sample mean delivery time of 38 minutes. What is this mean delivery time expressed as a z statistic? Interpret the z statistic.

What if sample size was 36?

A

Standard error: σ/√ N
so 12/√16=3 —> plug into z statistic

z statistic: z=(M-μ*M)/σM

so

z=38-30/3

standard error=12/4= 3

z statistic=38-30/3= 2.67

Thus, the mean delivery time is 2.67 standard errors from the mean.

There would be a smaller SD, and the Z statistic would be bigger.

Data Analysis exam 2 (3 decks)

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