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Hypothesis Tests with Means of Samples ,[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
The Distribution of Means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Building a Distribution of Means ,[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Determining the Characteristics of a Distribution of Means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Mean of a Distribution of Means ,[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Example 2 Copyright © 2011 by Pearson Education, Inc. All rights reserved
  die 1 die 2 Ave.   die 1 die 2 Ave.   die 1 die 2 Ave. 1 1 1 1 13 3 1 2 25 5 1 3 2 1 2 1.5 14 3 2 2.5 26 5 2 3.5 3 1 3 2 15 3 3 3 27 5 3 4 4 1 4 2.5 16 3 4 3.5 28 5 4 4.5 5 1 5 3 17 3 5 4 29 5 5 5 6 1 6 3.5 18 3 6 4.5 30 5 6 5.5 7 2 1 1.5 19 4 1 2.5 31 6 1 3.5 8 2 2 2 20 4 2 3 32 6 2 4 9 2 3 2.5 21 4 3 3.5 33 6 3 4.5 10 2 4 3 22 4 4 4 34 6 4 5 11 2 5 3.5 23 4 5 4.5 35 6 5 5.5 12 2 6 4 24 4 6 5 36 6 6 6
20   19   18   17   16   15   14   13   12   11   10   9   8   7   6   5     4         3             2                 1                                                 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 36 samples mean  f 1 1 1.5 2 2 3 2.5 4 3 5 3.5 6 4 5 4.5 4 5 3 5.5 2 6 1
20   19   18   17   16   15   14   13   12   11     10     9         8         7             6             5                 4                 3                     2                     1                                                     1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 72 samples   mean f 1 2 1.5 4 2 6 2.5 8 3 10 3.5 12 4 10 4.5 8 5 6 5.5 4 6 2
20   19   18   17     16     15     14         13         12         11             10             9             8                 7                 6                 5                     4                     3                     2                         1                                                     1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 108 samples   mean f 1 3 1.5 6 2 9 2.5 12 3 15 3.5 18 4 15 4.5 12 5 9 5.5 6 6 3
48     47     46     45     44     43     42     41     40     39         38         37         36         35         34         33         32         31             30             29             28             27             26             25             24             23                 22                 21                 20                 19                 18                 17                 16                 15                     14                     13                     12                     11                     10                     9                     8                     7                         6                         5                         4                         3                         2                         1                                                     1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 288 samples   mean f 1 8 1.5 16 2 24 2.5 32 3 40 3.5 48 4 40 4.5 32 5 24 5.5 16 6 8
[object Object],[object Object],The distribution of a pop. of individuals The distribution of a sample taken from pop.  The distribution of means of samples taken from pop.
Variance of a Distribution of Means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Standard Deviation of a Distribution of Means ,[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Variance of a Distribution of Means ,[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Variance of a Distribution of Means ,[object Object],[object Object],[object Object]
Standard Deviation of a Distribution of Means Copyright © 2011 by Pearson Education, Inc. All rights reserved Pop. SD = 2.5 in.
The Shape of a Distribution of Means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
[object Object],[object Object]
  die 1 f 1 1 1 2 2 1 3 3 1 4 4 1 5 5 1 6 6 1 6               5               4               3               2               1                                 1 2 3 4 5 6
20   19   18   17   16   15   14   13   12   11   10   9   8   7   6   5     4         3             2                 1                                                 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 36 samples mean  f 1 1 1.5 2 2 3 2.5 4 3 5 3.5 6 4 5 4.5 4 5 3 5.5 2 6 1
Review of the Three Kinds of Distributions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Hypothesis Testing with a Distribution of Means: The Z Test ,[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Figuring the Z Score of a Sample’s Mean on the Distribution of Means ,[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Figuring the Z Score of a Sample’s Mean on the Distribution of Means ,[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Figuring the Z Score of a Sample’s Mean on the Distribution of Means ,[object Object],[object Object],[object Object]
Steps for Hypothesis Testing ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Example of Steps for Hypothesis Testing: Step 1 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 3 ,[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 3 ,[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 4 ,[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 5 ,[object Object],Z =3.75
Example of Steps for Hypothesis Testing: Step 5 ,[object Object],[object Object],[object Object]
Steps for Hypothesis Testing ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
After-school example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 3 ,[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 3 ,[object Object],[object Object],[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 4 ,[object Object],[object Object]
Example of Steps for Hypothesis Testing: Step 5 ,[object Object]
Example of Steps for Hypothesis Testing: Step 5 ,[object Object],[object Object],[object Object],[object Object]
Hypothesis Tests about Means of Samples in Research Articles ,[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Advanced Topic: Estimation and Confidence Intervals ,[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Range of Possible Means Likely to Include the Population Mean ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Figuring the 95% and 99% Confidence Intervals ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved
Example of Figuring the 99% Confidence Interval ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example of Figuring the 95% Confidence Interval ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Confidence Intervals In Research Articles ,[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved

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Aron chpt 6 ed revised

  • 1.
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  • 6. Example 2 Copyright © 2011 by Pearson Education, Inc. All rights reserved
  • 7.   die 1 die 2 Ave.   die 1 die 2 Ave.   die 1 die 2 Ave. 1 1 1 1 13 3 1 2 25 5 1 3 2 1 2 1.5 14 3 2 2.5 26 5 2 3.5 3 1 3 2 15 3 3 3 27 5 3 4 4 1 4 2.5 16 3 4 3.5 28 5 4 4.5 5 1 5 3 17 3 5 4 29 5 5 5 6 1 6 3.5 18 3 6 4.5 30 5 6 5.5 7 2 1 1.5 19 4 1 2.5 31 6 1 3.5 8 2 2 2 20 4 2 3 32 6 2 4 9 2 3 2.5 21 4 3 3.5 33 6 3 4.5 10 2 4 3 22 4 4 4 34 6 4 5 11 2 5 3.5 23 4 5 4.5 35 6 5 5.5 12 2 6 4 24 4 6 5 36 6 6 6
  • 8. 20   19   18   17   16   15   14   13   12   11   10   9   8   7   6   5     4         3             2                 1                                                 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 36 samples mean  f 1 1 1.5 2 2 3 2.5 4 3 5 3.5 6 4 5 4.5 4 5 3 5.5 2 6 1
  • 9. 20   19   18   17   16   15   14   13   12   11     10     9         8         7             6             5                 4                 3                     2                     1                                                     1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 72 samples   mean f 1 2 1.5 4 2 6 2.5 8 3 10 3.5 12 4 10 4.5 8 5 6 5.5 4 6 2
  • 10. 20   19   18   17     16     15     14         13         12         11             10             9             8                 7                 6                 5                     4                     3                     2                         1                                                     1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 108 samples   mean f 1 3 1.5 6 2 9 2.5 12 3 15 3.5 18 4 15 4.5 12 5 9 5.5 6 6 3
  • 11. 48     47     46     45     44     43     42     41     40     39         38         37         36         35         34         33         32         31             30             29             28             27             26             25             24             23                 22                 21                 20                 19                 18                 17                 16                 15                     14                     13                     12                     11                     10                     9                     8                     7                         6                         5                         4                         3                         2                         1                                                     1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 288 samples   mean f 1 8 1.5 16 2 24 2.5 32 3 40 3.5 48 4 40 4.5 32 5 24 5.5 16 6 8
  • 12.
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  • 17. Standard Deviation of a Distribution of Means Copyright © 2011 by Pearson Education, Inc. All rights reserved Pop. SD = 2.5 in.
  • 18.
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  • 20.   die 1 f 1 1 1 2 2 1 3 3 1 4 4 1 5 5 1 6 6 1 6               5               4               3               2               1                                 1 2 3 4 5 6
  • 21. 20   19   18   17   16   15   14   13   12   11   10   9   8   7   6   5     4         3             2                 1                                                 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 36 samples mean  f 1 1 1.5 2 2 3 2.5 4 3 5 3.5 6 4 5 4.5 4 5 3 5.5 2 6 1
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