Homework Sourse1 In each case A B and C find the Critical Point Rejection R
1) In each case, A, B, and C, find the Critical Point, Rejection Region, and compute the P-Value
| A | B | C | |
| H0 | |||
| Ha |
Solution
Hypothesis Testing: Grades of a class are 75, 76, 80, 65, 69, 72, 75, 8, 90. Assume grades come from a Normal population. Given , remember that . Use \"z-score table\" and \"student\'s t-score table\" when needed.
A
B
C
H0
Ha
1) In each case, A, B, and C, find the Critical Point, Rejection Region, and compute the P-Value
Sample mean = 67.78
A this is upper tail test
Critical Point z = 1.645
Rejection Region : if the calculated z > 1.645 Reject Null hypothesis
the P-Value
the test statistic z = (67.78-74)/(10/sqrt(9)) = -1.866
the P-Value =0.969, do not reject null hypothesis
B this is lower tail test
Critical Point z = -1.645
Rejection Region : if the calculated z < -1.645 Reject Null hypothesis
the P-Value
the test statistic z= (67.78-74)/(10/sqrt(9)) = -1.866
the P-Value =0.031, reject null hypothesis
C this is two tail test
Critical Points z = -1.96 and 1.96
Rejection Region : if the calculated z < -1.96 or z > 1.96 Reject Null hypothesis
the P-Value
the test statistic z = (67.78-74)/(10/sqrt(9)) = -1.866
the P-Value =0.062, Do not reject null hypothesis
2) Repeat (1) if is unkown (use t-value)
Sample mean = 67.78
Sample sd =23.49
DF=9-1=8
A this is upper tail test
Critical Point t = 1.86
Rejection Region : if the calculated t > 1.86 Reject Null hypothesis
the P-Value
the test statistic t= (67.78-74)/(23.49/sqrt(9)) = -0.79
the P-Value =0.775, do not reject null hypothesis
B this is lower tail test
Critical Point t= -1.645
Rejection Region : if the calculated t < -1.86 Reject Null hypothesis
the P-Value
the test statistic t= (67.78-74)/(23.49/sqrt(9)) = -0.79
the P-Value =0.2249, do not reject null hypothesis
C this is two tail test
Critical Points t= -2.31 and 2.31
Rejection Region : if the calculated t < -2.31 or t > 2.31 Reject Null hypothesis
the P-Value
the test statistic t== (67.78-74)/(23.49/sqrt(9)) = -0.79
the P-Value =0.4499, Do not reject null hypothesis
| A | B | C | |
| H0 | |||
| Ha |
