Captain Psychology

Statistics

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Practice z Scores

Item 1

Calculate the z-score, assuming:

X = 10
mean = 50
stdev = 10

z score _____

 

Item 2

Calculate the z-score, assuming:

X = 80
mean = 50
stdev = 15

X – mean _____
z score _____

 

Item 3

Calculate the z-score, assuming:

X = 112
mean = 100
stdev = 15

X – mean _____
z score _____

 

Item 4

Calculate the raw score, assuming:

z = 1.5
mean = 115
stdev = 10

z * stdev _____
X _____

 

Item 5

Calculate the raw score, assuming:

z = -1.37
mean = 100
stdev = 20

z * stdev _____
X _____

 

Item 6

Calculate the raw score, assuming:

z = -1.37
mean = 100
stdev = 20

X _____

 

 

ANSWERS

Item 1

Calculate the z-score, assuming:
X = 10
mean = 50
stdev = 10
X – mean = – 40
z score = – 4.

Item 2

Calculate the z-score, assuming:
X = 80
mean = 50
stdev = 15
X – mean = 30
z score = 2.0

Item 3

Calculate the z-score, assuming:

X = 112
mean = 100
stdev = 15
X – mean = 12
z score = .80

Item 4

Calculate the raw score, assuming:
z = 1.5
mean = 115
stdev = 10
z * stdev = 15
X = 130

Item 5

Calculate the raw score, assuming:

z = -1.37
mean = 100
stdev = 20
z * stdev = 27.4
X = 72.6

Item 6

Calculate the raw score, assuming:
z =  2.54
mean = 80
stdev = 20
X = 130.8
2.54*20 = 50.8
50.8 + 80 = 130.8

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Practice t Tests

Independent Student t

Item #1

Calculate am independent t-test for the following data:

X1 X2
6             12
4               4
2               7
3             10
9               5
6               8
5               3

Mean of group 1 _____

Mean of group 2 _____

Difference between the means _____

SS of group 1 _____

SS of group 2 _____

n(n-1) _____

t = _____

How many degrees of freedom (df) at in this study_____

What is the critical value for t (2 tailed, .05 alpha) _____

Is the t significant _____

 

Item #2

Calculate am independent t-test for the following data:

X1 X2
15          3
11          5
8          4
12          2
7          6

Mean of group 1 _____

Mean of group 2 _____

SS of X1 _____

SS of X2 _____

t = _____

 

Item #3

Calculate am independen t-test for the following data:

X1 X2
6           3
7           5
6           3
8           2
4           7
11           4

t = _____

How many degrees of freedom (df) at in this study ____

What is the critical value for t (2 tailed, .05 alpha) _____

Is the t significant? _____

 

Item #4

Which students do significantly better in reading (Words per minute):

High Sch     College
7                     5
4                     3
6                     1
6                   11
3                     8
2                     8
1                   13
6                     9

t =

.

Item #5

Which cars are the safest (accidents):

Foreign      Domestic
16             1
14             3
12             9
18           11
12             6
7             1

t =

Item #6

Which dogs are the meanest (bites per minute):

Big             Little
1                   6
4                   3
3                   9
8                 11
2                 16
7                 11
5                 22
3                   7

t =

ANSWERS

Item #1

Calculate am independent t-test for the following data:

X1            X2
6             12
4               4
2               7
3             10
9               5
6               8
5               3

Mean of group 1        5

Mean of group 2       7

Difference between the means   2

SS of group 1           32

SS of group 2           64

n(n-1)                      42

t = 1.32

How many degrees of freedom (df) at in this study   N-2 = 12

What is the critical value for t (2 tailed, .05 alpha)      2.18

Is the t significant       No. The calculated value (1.32) is not equal to (or bigger) that the critical value (2.18). The differences between the groups is likely to be due to chance.

 

Item #2

Calculate am independent t-test for the following data:

X1            X2
15          3
11          5
8          4
12          2
7          6

Mean of group 1     10.60

Mean of group 2      4.00

SS of X1     41.20

SS of X2    10

t =   4.13

 

Item #3

Calculate am independen t-test for the following data:

X1              X2
  6           3
7           5
6           3
8           2
4           7
11           4

t = 2.48

How many degrees of freedom (df) at in this study     10

What is the critical value for t (2 tailed, .05 alpha)       2.23

Is the t significant? Yes

 

Item #4

Which students do significantly better in reading (Words per minute):
High Sch College
7                     5
4                     3
6                     1
6                   11
3                     8
2                     8
1                   13
6                     9
t = 1.77
Which students do significantly better in reading:

Item #5

Which cars are the safest (accidents):
Foreign Domestic
16             1
14             3
12             9
18           11
12             6
7             1
t = 3.45
Which cars are the safest (accidents):

Item #6

Which dogs are the meanest (bites per minute):
Big Little
1                   6
4                   3
3                   9
8                 11
2                 16
7                 11
5                 22
3                   7
t = 2.37
Which dogs are the meanest (bites per minute):

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Practice Regression

Linear Regression

Item 1

If there are 6 petals on a flower, how much will an elephant plant weigh (in pounds):

Petals Weight
8            1
5            6
2            7
1            8
9            2

SSx = _____
SSy = _____
SSxy = ____
a = _____
b = _____

 

Item 2

If there are 9 dolls, how many truckes will a child have:
Trucks Dolls
12                   11
8                     7
6                     5
2                     1
4                     3
9                     9
14                   15

a = _____
b = _____
r = _____
standard error of estimate (SEE) = _____

 

Item 3

If your high school GPA is 3.3, what would you predict your college GPA to be:

High Schl College
1.0             3.9
2.5             3.7
3.3             1.4
4.0             1.0
2.3             2.9

a = _____
b = _____

 

Item 4

If there are 22 ducks, how many cows will the farmer own:

Ducks Cows
3                     11
6                      6
9                      8
11                      1
15                      2
4                     10
5                      7

a = _____
b = _____
r = _____
standard error of estimate (SEE) = _____

 

Item 5

If there are 3 doctors, how many nurses will a hospital have

Doctors Nurses
9              15
4                5
2                3
11               1
16             18
17             10

a = _____
b = _____
see = _____

 

Item 6

If there are 7 professors, how many classes will be taught:

Professors Classes
1                     3
4                     8
12                   13
8                     2
7                     8
7                     9
a =
b =
r =
see =
If X (professors) is 7, Y (classes) will be =<

 

Item 7

If there are 150 candles, how many flowers will a wedding have?

Candles Flowers
22                 2
8                 4
6                 9
3               11
12                 4
1                 6
16               19

a =
b =
How accurate is your prediction? (see) =
If X is 150 (candles), Y (flowers) will be

 

Item 8

How much will tuition (in thousands) be in 1997:
Year Tuition
1990             1
1991             3
1992             9
1993           12
1994           16
a =
b =
[Hint: use the last digit of the year or convert Years to your own integers]
If X (year) is 7, Y (tuition) will be =

 

ANSWERS

Item 1

If there are 6 petals on a flower, how much will an elephant plant weigh (in pounds):

Petals Weight
8                 1
5                 6
2                 7
1                 8
9                 2

SSx = 50
SSy = 38.8
SSxy = – 42
a = 9
b = – .84

with an r of – .95, this is a strong correlation and a good predictor

6 pearls predict s 3.86 pounds

 

Item 2

If there are 9 dolls, how many truckes will a child have:
Trucks Dolls
12                   11
8                     7
6                     5
2                     1
4                     3
9                     9
14                   15

Dolls are predicting Trucks

a =.  1.47
b = .88
r = .99
standard error of estimate (SEE) = .57

9 dolls predicts 9.36 trucks

 

Item 3

If your high school GPA is 3.3, what would you predict your college GPA to be:

High Schl College
1.0             3.9
2.5             3.7
3.3             1.4
4.0             1.0
2.3             2.9

a = 5.33
b = – 1.05
r = – .90
standard error of estimate (SEE) = .68

High school grades are not a predictor of college grades

3.3 predicts 1.87

 

Item 4

If there are 22 ducks, how many cows will the farmer own:

Ducks Cows
3                     11
6                      6
9                      8
11                      1
15                      2
4                     10
5                      7

a = 8.17
b = – .17
r = – .17
standard error of estimate (SEE) = 4.89

22 ducks predicts 4.35 cows

 

Item 5

If there are 3 doctors, how many nurses will a hospital have

Doctors Nurses
9              15
4                5
2                3
11               1
16             18
17             10
a = 2.42
b = .63
see = 6.28

With an r of .57, not going to predict we’ll.

3 doctors predicts 4.33 nurses

Item 6

If there are 7 professors, how many classes will be taught:

Professors         Classes
1                     3
4                     8
12                   13
8                     2
7                     8
7                     9

a =   2.82
b =    .67
r =    .61
see = 3.60

If X (professors) is 7, Y (classes) will be = 7.5

 

Item 7

If there are 150 candles, how many flowers will a wedding have:

Candles       Flowers
22                 2
8                 4
6                 9
3               11
12              4
1                 6
16               19

a =   8.24
b =  – .04

How accurate is your prediction? (see) =  6.36

If X is 150 (candles), Y (flowers) will be = 2.27

 

Item 8

How much will tuition (in thousands) be in 1997:
Year          Tuition
1990             1
1991             3
1992             9
1993           12
1994           16

a =    .40
b =  3.90
Hint: use the last digit of the year or convert Years to your own integers

If X (year) is 7, Y (tuition) will be = 27.7

 

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Practice Dispersion

Range, Sun of Squares, Variance & Stdev

Item 1

Calculate the range of the following scores:

19
15
8
5
5
2

High Score _____
Low Score _____
Range _____

 

Item 2

Calculate the range and SS of the following scores:

11
9
8
7
5
7

High Score _____
Low Score _____
SumX             _____
SumX2 _____
(SumX)2 _____
N               _____
SS              _____
variance    _____

 

Item 3

Calculate the variance of the following population:

18
9
7
5
4
2

SumX           _____
SumX2 _____
(SumX)2 _____
N                 _____
SS                _____
variance      _____

 

Item 4

Calculate the SS, variance and stdev of the following population:

3
18
9
6
10
6
4

SumX             _____
SumX2 _____
(SumX)2 _____
N               _____
SS              _____
variance      _____

 

Item 5

Calculate the range, SS, variance and stdev of the following sample:

12
3
9
5
5
5
7
11
14
– 1

Range     _____
N            _____
SS          _____
variance  _____

 

Item 6

Calculate the SS of the following scores:

2
2
2
5
5
5
7

SS =

 

Item 7

Calculate the range and SS of the following scores:

2
5
7
3
3
13
19
4

range =
SS =

 

Item 8

Calculate the SS and stdev. of the following population scores:

11
10
12
2
4
7

SS =
variance =

 

Item 9

Calculate the stdev. of the following population:

14
3
5
8
6
9

stdev. =

 

Item 10

Calculate the SS of the following sample:

5
7
7
6
3
2

SS =

ANSWERS

Item 1

Calculate the range of the following scores:

19
15
8
5
5
2

High Score 19
Low Score    2
Range        17

 

Item 2

Calculate the range and SS of the following scores:

11
9
8
7
5
7

High Score      11
Low Score         5
SumX              47
SumX2          389
(SumX)2      2209
N                      6
SS              20.83
variance    3.47 (if a population) or 4.17 (if a sample)

 

Item 3

Calculate the variance of the following population:

18
9
7
5
4
2

SumX              45
SumX2          499
(SumX)2      2025
N                      6
SS                 161.50
variance         26.92

 

Item 4

Calculate the SS, variance and stdev of the following population:

3
18
9
6
10
6
4

SumX                56
SumX2            602
(SumX)2            3136
N                       7
SS                  154
variance           22
stdev                 4.69

 

Item 5

Calculate the range, SS, variance and stdev of the following sample:

12
3
9
5
5
5
7
11
14
– 1

Range     15
N            10
SS          186
variance  20.67 (it is a sample, so it is Sum of Squares divided by N-1)
The standard deviation would be 4.55

 

 

Item 6

Calculate the SS of the following scores:

2
2
2
5
5
5
7

SS = 24

 

Item 7

Calculate the range and SS of the following scores:

2
5
7
3
3
13
19
4

range = 17
SS = 250

 

Item 8

Calculate the SS and stdev of the following population scores:

11
10
12
2
4
7

SS = 81.33
variance = 13.56

 

Item 9

Calculate the stdev. of the following population:

14
3
5
8
6
9

SumX = 45
SS = 73.50
variance = 12.25
stdev. = 3.50

 

Item 10

Calculate the SS of the following sample:

5
7
7
6
3
2

SS = 22.00

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Practice Correlation

Pearson r

Item 1

What is the correlation between these two variables:
Stress                Sense of Humor
4                             2
10                             8
12                            11
5                             3
7                             8
6                             7
2                             3
14                            13

SSx = _____
SSy = _____
SSxy = _____
r = _____

 

Item 2

What is the correlation between these two variables:
Laughter                      Statistics
11                              19
3                                6
5                                6
15                              12
7                                8
6                                7
9                              14

SSx = _____
SSy = _____
SSxy = _____
r = _____

 

Item 3

How much variance is accounted for between these two variables:

Strength                   Speed
12                           3
9                           7
6                           9
3                         11
1                         15
7                           6

SSx = _____
SSy = _____
SSxy = _____
r = _____
rsquared = _____

 

Item 4

What is the correlation between these two variables:

Strength                Peace
2                         2
6                         5
7                         8
14                       19
15                       12
9                         8
4                         5

SSx = _____
SSy = _____
SSxy = _____
r = _____
rsquared = _____

 

Item 5

How much variance is NOT accounted for between these two variables

Strength Anxiety
2                     3
9                     7
3                     4
1                     1
7                   12
SSx =     _____
SSy =     _____
SSxy =   _____
r =         _____
r2 =        _____
1 – r2 = _____

 

Item 6

Is there a significant relationship between the number of petals on a flower and how much the elephant plant weighs
Petals Weight
18                     1
15                     7
8                   11
6                     6
4                   18
2                   22
SSx =     _____
SSy =     _____
SSxy =   _____
r =         _____
r2 =        _____

 

Item 7

What percent of variance do love and peace have in common

Love Peace
12                     1
22                     3
8                     0
19                     1
2                   11
9                     4
7                     5
SSx =     _____
SSy =     _____
SSxy =   _____
r =         _____
r2 =        _____

 

ANSWERS

Item 1

What is the correlation between these two variables:
Stress         Sense of Humor
4                     2
10                     8
12                   11
5                     3
7                     8
6                     7
2                     3
14                   13
SSx =    120.00
SSy =    110.88
SSxy =  108.50
r =   .94

 

Item 2

What is the correlation between these two variables:
Laughter     Statistics
11                 19
3                   6
5                   6
15                 12
7                   8
6                   7
9                 14
SSx =     98.00
SSy =   145.43
SSxy =   85.00
r =   .71

 

Item 3

How much variance is accounted for between these two variables:

Strength        Speed
12                 3
9                 7
6                 9
3               11
1               15
7                 5
SSx =      79.33
SSy =      87.50
SSxy =  – 80.00
r =    – .96
r2 =   .92 or 92% of the mutual variance is accounted for

 

Item 4

What is the correlation between these two variables:

Strength         Peace
2                     2
6                     5
7                     8
14                   19
15                   12
9                     8
4                     5
SSx =     142.86
SSy =     189.71
SSxy =   147.57
r =   .896
Just for practice here is the r2 =   .80 or 80% of the mutual variance

 

Item 5

How much variance is NOT accounted for between these two variables:

Strength   Anxiety
2                     3
9                     7
3                     4
1                     1
7                   12

SSx =     47.20
SSy =     73.20
SSxy =   47.20
r =              .80
r2 =       .65 or 65%

1 – r2 = .35 or 35

 

Item 6

Is there a significant relationship between the number of petals on a flower and how much the elephant plant weighs:
Petals      Weight
18                     1
15                     7
8                   11
6                     6
4                   18
2                   22

SSx =  200.83
SSy =  310.83
SSxy = – 211.17
r =  – .85
r2 = .71
Check r against the Critical values of the Pearson r table using 4 degrees of freedom = .811
Since r of .85 is larger than the table r of .81, this correlation is significant and the relationship you see is not likely to be due to chance.

 

Item 7

What percent of variance do love and peace have in common

Love Peace
12                     1
22                     3
8                     0
19                     1
2                   11
9                     4
7                     5
SSx =  245.43
SSy =     83.71
SSxy =   – 92.14
r =         – .59
r2 =        34%

 

 

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Practice ANOR

Analysis of Regression

Item 1

Calculate an Analysis of Regression on the following data, where Reading is predicting Education:

Reading     Education
15                 11
7                  8
2                  5
9                  4
4                  4
11                  9

What is the Pearson r: _______

Perform the following calculations:

SS     df     ms

Regression         ____     ____     ____

Error                 ____     ____     ____

TOTAL             ____     __

What is the F for this test: ____________

 

Item 2

Calculate an Analysis of Regression on the following data, where TV watching predicts Violence:

Television Violence
2                       7
4                     14
8                     12
13                       8
16                       5
19                       2

Perform the following calculations:

SS df ms

Regression         ____     ____     ____

Error                 ____     ____     ____

TOTAL             ____     ____

What is the F for this test: ______

 

Item 3

To discover if TV watching has a significant impact on people’s shyness, use the following information, perform an Analysis of Regression and complete the following summary table:

r= .88
SSx = 50
SSy = 74
N = 12

SS df ms

Regression         ____     ____     ____

Error                 ____     ____     ____

TOTAL             ____     ____

What is the F for this test: ___________

What is the critical value for F: _________

Is the F significant? ________

 

Item 4

To discover if learning statistics has a significant impact on people’s friendliness, use the following information, perform an Analysis of Regression and complete the following summary table:

r= .32
SSx = 30
SSy = 66
N = 15

SS df ms

Regression         ____     ____     ____

Error                 ____     ____     ____

TOTAL             ____     ____

What is the F for this test: ___________

Is the critical value for F: ____________

Item 5

To discover if education has a significant impact on people’s income, use the following information, perform an Analysis of Regression and complete the following summary table:
r= .73
SSx = 98
SSy = 44
N = 13
SS df ms
Regression      ____     ____    ____
Error               ____     ____     ____
TOTAL             ____     ____
What is the F for this test: ___________
What is the critical value for F: ________
Is the F significant? _________

Item 6

To discover if music lessons have a significant impact on people’s intelligence, use the following information, perform an Analysis of Regression and complete the following summary table:
r= – .56
SSx = 111.3
SSy = 87.8
N = 16
SS df ms
Regression         ____     ____     ____
Error                   ____     ____     ____
TOTAL                 ____    ____
What is the F for this test: ___________
What is the critical value for F: ________
Is the F significant? _________

ANSWERS

Item 1

Calculate an Analysis of Regression on the following data, where Reading is predicting Education:

Reading     Education
15                 11
7                  8
2                  5
9                  4
4                  4
11                  9

What is the Pearson r: .78

Perform the following calculations:

                            SS           df        ms

Regression         26.04         1      26.04

Error                  16.80         4        4.20

TOTAL              42.84         5        8.57

What is the F for this test:   6.20

 

Item 2

Calculate an Analysis of Regression on the following data, where TV watching predicts Violence:

Television       Violence
2                       7
4                     14
8                     12
13                       8
16                       5
19                       2

Perform the following calculations:

                             SS           df     ms

Regression         50.86          1     50.86

Error                  47.14          4     11.78

TOTAL             98.00          5     19.60

What is the F for this test:   4.32

 

 

Item 3

To discover if TV watching has a significant impact on people’s shyness, use the following information, perform an Analysis of Regression and complete the following summary table:

r= .88

SSx = 50

SSy = 74

N = 12

                        SS        df        ms

Regression       57.31     1       57.31

Error                16.69   10        1.67

Total                74        11        6.73

                        F =       34.33

Is the critical value for F:   4.96

Is the F significant?  Yes

 

Item 4

To discover if learning statistics has a significant impact on people’s friendliness, use the following information, perform an Analysis of Regression and complete the following summary table:

r= .32

SSx = 30

SSy = 66

N = 15

                         SS        df        ms

Regression         6.76      1         6.76

Error                59.24    13        4.56

Total                66         14        4.71

                        F =       1.48

What is the critical value for F:   4.67

Is the F significant?  No

Item 5

To discover if education has a significant impact on people’s income, use the following information, perform an Analysis of Regression and complete the following summary table:

r= .73
SSx = 98
SSy = 44
N = 13

SS          df          ms

Regression          23.45        1       23.45
Error                   20.55      11        1.87
Total                   44           12         3.67

F = 12.55
What is the critical value for F:    4.84
Is the F significant?  Yes

 

Item 6

To discover if music lessons have a significant impact on people’s intelligence, use the following information, perform an Analysis of Regression and complete the following summary table:

r= -.56
SSx = 111.3
SSy = 87.8
N = 16

SS          df           ms
Regression      27.53         1        27.53
Error               60.27       14         4.30
Total               87.80       15         5.85

 

F = 6.40
What is the critical value for F:   4.60
Is the F significant?  Yes