a)
To find:
The Z(critical) value for the given situation.
Solution:
The Z(critical) values are given in Table
Alpha ( 
Form of the Test  Z(critical) 
0.05  Onetailed 

0.10  Twotailed 

0.06  Twotailed 

0.01  Onetailed 

0.02  Twotailed 
Given:
The given table of alpha values is,
Alpha ( 
Form of the Test  Z(critical) 
0.05  Onetailed  
0.10  Twotailed  
0.06  Twotailed  
0.01  Onetailed  
0.02  Twotailed 
Description:
The critical region of a sampling distribution is the area that includes the unlikely sample outcomes.
The critical Z values are the areas under the standard normal curve.
For onetailed critical values, the area is only on one side and the whole value of
For twotailed critical values, the area is equally divided on both the sides and the value of
Calculation:
The given table of alpha values is,
Alpha ( 
Form of the Test  Z(critical) 
0.05  Onetailed  
0.10  Twotailed  
0.06  Twotailed  
0.01  Onetailed  
0.02  Twotailed 
Table
The Z(critical) are obtained from the critical value table for standard normal variates.
For
Or,
Thus, for
For
And,
Thus, for
For
And,
Thus, for
For
Or,
Thus, for
For
And,
Thus, for
The obtained critical values are tabulated as,
Alpha ( 
Form of the Test  Z(critical) 
0.05  Onetailed 

0.10  Twotailed 

0.06  Twotailed 

0.01  Onetailed 

0.02  Twotailed 
Table
Conclusion:
The Z(critical) values are given in Table
Alpha ( 
Form of the Test  Z(critical) 
0.05  Onetailed 

0.10  Twotailed 

0.06  Twotailed 

0.01  Onetailed 

0.02  Twotailed 
b)
To find:
The t(critical) value for the given situation.
Solution:
The t(critical) values are given in Table
Alpha ( 
Form of the Test  N  t(critical) 
0.10  Twotailed 
31  
0.02  Twotailed 
24  
0.01  Twotailed 
121  
0.01  Onetailed 
31  
0.05  Onetailed 
61 
Given:
The given table of alpha values is,
Alpha ( 
Form of the Test  N  t(critical) 
0.10  Twotailed  31  
0.02  Twotailed  24  
0.01  Twotailed  121  
0.01  Onetailed  31  
0.05  Onetailed  61 
Description:
The critical region of a sampling distribution is the area that includes the unlikely sample outcomes.
The critical t values are the areas under the curve of tdistribution.
For onetailed critical values, the area is only on one side and the whole value of
For twotailed critical values, the area is equally divided on both the sides and the value of
Calculation:
The given table of alpha values is,
Alpha ( 
Form of the Test  N  t(critical) 
0.10  Twotailed  31  
0.02  Twotailed  24  
0.01  Twotailed  121  
0.01  Onetailed  31  
0.05  Onetailed  61 
Table
The t(critical) values are obtained from the tdistribution table with the given value of
For
And,
Thus, for
For
And,
Thus, for
For
And,
Thus, for
For
Or,
Thus, for
For
Or,
Thus, for
The obtained critical values are tabulated as,
Alpha ( 
Form of the Test  N  t(critical) 
0.10  Twotailed 
31  
0.02  Twotailed 
24  
0.01  Twotailed 
121  
0.01  Onetailed 
31  
0.05  Onetailed 
61 
Table
Conclusion:
The t(critical) values are given in Table
Alpha ( 
Form of the Test  N  t(critical) 
0.10  Twotailed 
31  
0.02  Twotailed 
24  
0.01  Twotailed 
121  
0.01  Onetailed 
31  
0.05  Onetailed 
61 
c)
To find:
The appropriate test statistics for the given situation.
Solution:
The Z(critical) and t(critical) values are given in Table
Population  Sample  Z(obtained) or t(obtained)  
1.  
2.  
3.  
4.  0.66  
5.  0.77 
Given:
The given table of information is,
Population  Sample  Z(obtained) or t(obtained)  
1.  
2.  
3.  
4.  
5. 
Formula used:
For large samples with single mean and given standard deviation, the Z value is given by,
Where,
N is the sample size.
For small samples with single sample mean and unknown standard deviation, the t value is given by,
Where,
N is the sample size.
For large samples with single sample proportions, the Z value is given by,
Where,
N is the sample size.
Calculation:
The given table of alpha values is,
Population  Sample  Z(obtained) or t(obtained)  
1.  
2.  
3.  
4.  
5. 
Table
For large samples with single mean and given standard deviation, the Z value is given by,
For sample mean
Substitute 2.20 for
Thus, the obtained Z value is
For small samples with single sample mean and unknown standard deviation, the t value is given by,
For sample mean
Substitute 16.8 for
Thus, the obtained t value is
For sample mean
Substitute 9.4 for
Thus, the obtained t value is
For large samples with single sample proportions, the Z value is given by,
For sample proportion
Substitute 0.60 for
Thus, the obtained Z value is
For sample proportion
Substitute 0.30 for
Thus, the obtained Z value is
The obtained critical values are tabulated as,
Population  Sample  Z(obtained) or t(obtained)  
1.  
2.  
3.  
4.  0.66  
5.  0.77 
Table
Conclusion:
The Z(critical) and t(critical) values are given in Table
Population  Sample  Z(obtained) or t(obtained)  
1.  
2.  
3.  
4.  0.66  
5.  0.77 
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