, find the critical value(s) for each situation and draw the appropriate figure showing the critical region. 1. a=0.01. left-tailed 2. a 5%, right-tailed 3. A two-tailed with a = 0.005

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Note: please refer to the given lesson
. find the critical value(s) for each situation and draw the appropriate figure
showing the critical region.
1. α=0.01. left-tailed
2. a 5%, right-tailed
3. A two-tailed with a=0.005
Transcribed Image Text:. find the critical value(s) for each situation and draw the appropriate figure showing the critical region. 1. α=0.01. left-tailed 2. a 5%, right-tailed 3. A two-tailed with a=0.005
Step 2: Determine the corresponding Z-value from the table.
a. For a left-tailed test, use the z value that corresponds to the area equivalent to a in the table.
For a right-tailed test, use the value that corresponds to the area equivalent to 1-a.
For a two-tailed test, use the value that corresponds to a/2 for the left value. It will be
negative. For the right value, use the value that corresponds to the area equivalent to 1 -a/2. It
will be positive.
b.
c.
Examples:
Using Table- A, find the critical value(s) for each situation and draw the appropriate figure, showing the
critical region.
0.9901.
1. a-0.10, left-tailed
Solution:
Step 1: Draw the figure and indicate the area.
Since this is a left- tailed test, the area
0.10 is located in the left tail, as
shown.
of
area of
2.575.
2. A right-tailed test with a = 0.005
Solution:
Step 1: Draw the figure and indicate the area.
Since this is a right-tailed test, the
0.005 is located in the right tail, as
shown.
Step 2: Determine the corresponding Z- Value from the table.
Step 2: Determine the corresponding Z-Value from the table.
Find the area closest to 0.1000 in Table A. In this Case, it is 0.1003. Find the Z- Value that
corresponds to the area 0.1003. It is 1.28.
3. A two-tailed test with a = 0.02
Solution:
Step 1: Draw the figure and indicate the area.
In this case, there are two areas
9.10
equivalent
-1.28
z
0.01.
STATISTICS AND PROBABILITY
3000
0
Find the area closest to 1-a, or 1-0.005-0.9950. In this case, it is 0.9949 or 0.9951.
The two z values corresponding to 0.9949 and 0.9951 are 2.57 and 2.58. Since 0.9950 is
halfway between these two values, find the average of the two value: (2.57+2.58)/2=
However, 2.58 is most often used.
0 9900
0
+2.58
0.005
+2.33
to a/2, or 0.02/2=0.01.
Step 2: Determine the corresponding Z- Value from the table.
For the left z critical value, find the area closest to 0.01. In this case, it is 0.0099.
For the right z critical value, find the area closest to 1-0.01 -0.9900. In this case, it is
Transcribed Image Text:Step 2: Determine the corresponding Z-value from the table. a. For a left-tailed test, use the z value that corresponds to the area equivalent to a in the table. For a right-tailed test, use the value that corresponds to the area equivalent to 1-a. For a two-tailed test, use the value that corresponds to a/2 for the left value. It will be negative. For the right value, use the value that corresponds to the area equivalent to 1 -a/2. It will be positive. b. c. Examples: Using Table- A, find the critical value(s) for each situation and draw the appropriate figure, showing the critical region. 0.9901. 1. a-0.10, left-tailed Solution: Step 1: Draw the figure and indicate the area. Since this is a left- tailed test, the area 0.10 is located in the left tail, as shown. of area of 2.575. 2. A right-tailed test with a = 0.005 Solution: Step 1: Draw the figure and indicate the area. Since this is a right-tailed test, the 0.005 is located in the right tail, as shown. Step 2: Determine the corresponding Z- Value from the table. Step 2: Determine the corresponding Z-Value from the table. Find the area closest to 0.1000 in Table A. In this Case, it is 0.1003. Find the Z- Value that corresponds to the area 0.1003. It is 1.28. 3. A two-tailed test with a = 0.02 Solution: Step 1: Draw the figure and indicate the area. In this case, there are two areas 9.10 equivalent -1.28 z 0.01. STATISTICS AND PROBABILITY 3000 0 Find the area closest to 1-a, or 1-0.005-0.9950. In this case, it is 0.9949 or 0.9951. The two z values corresponding to 0.9949 and 0.9951 are 2.57 and 2.58. Since 0.9950 is halfway between these two values, find the average of the two value: (2.57+2.58)/2= However, 2.58 is most often used. 0 9900 0 +2.58 0.005 +2.33 to a/2, or 0.02/2=0.01. Step 2: Determine the corresponding Z- Value from the table. For the left z critical value, find the area closest to 0.01. In this case, it is 0.0099. For the right z critical value, find the area closest to 1-0.01 -0.9900. In this case, it is
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