More Practice Problem ANSWERS: 1-Way ANOVA

Item 3

Which is the best coffee (most cups ordered):

Blue-Label   Green-Label     Red-Label 
            13              1              5 
              4              1              2 
            10              2              2 
            13              2              2 
            11              2              6 
              3              4              4

Sum        54         12          21                87
Sum X² 584         30          89              703
N              6           6            6                18
SS           98          6          15.50          119.50

 

 

                       SS          df         ms
Between       163.00       2       81.50
Within          119.50     15         7.97
Total             282.50     17       16.62

 F = 10.23

Critical value of F = 3.68. F is significant.

Which is the best coffee. You’ll have to do t-tests to find out. But looking at the numbers above, you can guess that Blue Label is most likely to be the big winner. But you’ll know more after you do the post tests.

 

 

Item 4

Which is candle lasts more days?

Non-Sented     Low-Sented   High-Sented
      3                 5                 8
      9                 1                 2
      5                 2                 6
    11                 5                 4

Sum         28              13                20             61
Sum X²  236              55              120           411
N               4                 4                  4             12
SS           40              12.75            20         72.75

 

SS        df        ms

Between         27.17      2        14.08

Within            72.75      9         8.08

Total               100.92  11        9.17                

 

F = 1.74

 Critical value of F = 4.26. F is not significant.

Which is candle lasts more days? No significant difference between them. Choose any.

 

 

 

NOW YOU CHOOSE
    Day9: 1-Way ANOVA
    Bit More About 1-Way ANOVA
    Even More About 1-Way ANOVA
    Calculate 1-Way ANOVA
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1        Sim2         Sim3
        Sim4        Sim5         Sim6
        Sim7        Sim8         Sim9
    Vocabulary
    Formulas
    Quiz 9
    Summary

Practice Problem ANSWERS: 1-Way ANOVA

Item 1 

Year in school and car accidents.

10th     11th    12th
   2        13        4
   9        17        8
   3        14        2
   1          9        1
   7         1         4

 

                      SS      df    ms

Between     150.53    2   75.27

Within        228.80  12   19.07

Total          379.33  14   27.10

F =   3.95

Which grade has the most car accidents: The critical value is 3.74, so F is significant. You can now do multiple t-tests to discover which means are significantly different from each other.

 

Item 2

House color and people’s stay (in years).

Blue    Green   Peach
  8        11         4
  7         9          8
  3         7          9
  1       18          2
  9       12          4

                   SS     df    ms

Between     116.13   2   58.07

Within        151.60  12  12.63

Total          267.73   14   19.12

F =   4.60

Which color of house is lived in the longest (in years)? The critical value is 3.74, so F is significant. You can now do multiple t-tests to discover which means are significantly different from each other.

 

NOW YOU CHOOSE
    Day9: 1-Way ANOVA
    Bit More About 1-Way ANOVA
    Even More About 1-Way ANOVA
    Calculate 1-Way ANOVA
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1        Sim2         Sim3
        Sim4        Sim5         Sim6
        Sim7        Sim8         Sim9
    Vocabulary
    Formulas
    Quiz 9
    Summary

Practice Problem ANSWERS: Dispersion

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

 

NOW YOU CHOOSE:
    Day 3: Dispersion
    A Bit More About Dispersion
    Even More About Dispersion
        Range
        MAD
        Sum of Squares
        Variance
        Standard Deviation
    How To Calculate
        Range
        MAD
        Sum of Squares
        Variance
        Standard Deviation
    Formulas For Dispersion
    Practice Problems
    More Practice Problems
    Basic Facts About Dispersion
    Vocabulary
    Quiz 3
    Summary

 

More Practice Problem ANSWERS: Regression

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 = 7.51

 

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

 

NOW YOU CHOOSE:

• Read A Bit More About Regression
• Read Even More About Regression
• Listen to Lecture 5 (coming soon)
• Practice Problems
• More Practice Problems
• Review Basic Facts About Regression
• Review Day 6 Vocabulary
• Review Day 6 Formulas
• Take Quiz 6
• Summary

More Practice Problem ANSWERS: Correlation

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 =    295.43
SSy =      83.71
SSxy = – 92.14
r =  – .59
r² = .34 or 34% of the variance in common

 

NOW YOU CHOOSE:
    Day 5: Correlation
    Bit More About Correlation
    Even More About Correlation
    Calculate Correlation
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1            Sim2             Sim3
        Sim4            Sim5             Sim6
        Sim7            Sim8             Sim9
    Basic Facts About Correlation
    Vocabulary
    Formulas
    Quiz 5
    Summary

  

More Practice Problem ANSWERS: t-Test

#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: No significant difference. The differences between student groups is likely to be due to chance.

 

 

#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): Domestic cars are significantly safer than foreign cars.

 

 

#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): Little dogs are significantly meaner.

 

NOW YOU CHOOSE:
    Day 8: Student’s t-Test
    Bit More About t-Test
    Even More About t-Test
    How to Calculate t-Test
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1           Sim2            Sim3
        Sim4           Sim5            Sim6
        Sim7           Sim8            Sim9
    Basic Facts About t-Test
    Vocabulary
    Formulas
    Quiz 8
    Summary

Practice Problem ANSWERS: t-Test

 

#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.

 

 

#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

 

 

#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

 

NOW YOU CHOOSE:
    Day 8: Student’s t-Test
    Bit More About t-Test
    Even More About t-Test
    How to Calculate t-Test
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1           Sim2            Sim3
        Sim4           Sim5            Sim6
        Sim7           Sim8            Sim9
    Basic Facts About t-Test
    Vocabulary
    Formulas
    Quiz 8
    Summary

More Practice Problem ANSWERS: ANOR

 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

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

NOW YOU CHOOSE:
    Day 7: Probability
    Bit More About Probability
    Even More About Probability
    Even More About ANOR
    Calculate ANOR
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1       Sim2        Sim3
    Basic Facts About Probability
    Vocabulary
    Formulas
    Quiz 7
    Summary

 

Practice Problem ANSWERS: ANOR

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

 

 

 

NOW YOU CHOOSE:
    Day 7: Probability
    Bit More About Probability
    Even More About Probability
    Even More About ANOR
    Calculate ANOR
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1       Sim2        Sim3
    Basic Facts About Probability
    Vocabulary
    Formulas
    Quiz 7
    Summary

Practice Problem ANSWERS: Regression

Item 1

Calculate the z-score, assuming:

X = 10
mean = 50
stdev = 10
X – mean = – 40 
z score = – 4.0

 

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

 

 

NOW YOU CHOOSE:

Read A Bit More About Regression
Read Even More About Regression
Listen to Lecture 5 (coming soon)
Practice Problems
More Practice Problems
Review Basic Facts About Regression
Review Day 6 Vocabulary
Review Day 6 Formulas
Take Quiz 6
Summary

 

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