Homework SourseConsider the following hypotheses H0 5000 The population is
Consider the following hypotheses:
H0: = 5,000
The population is normally distributed with a population standard deviation of 690. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can \"reject/do not reject\" the null hypothesis at the 10% significance level. Use http://lectures.mhhe.com/connect/0077639472/Table/table1.jpg . (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round \"test statistic\" values to 2 decimal places and \"p-value\" to 4 decimal places.)
| Consider the following hypotheses: |
Solution
H0: = 5,000
HA: 5,000
The population is normally distributed with a population standard deviation of 690. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can \"reject/do not reject\" the null hypothesis at the 10% significance level. Use http://lectures.mhhe.com/connect/0077639472/Table/table1.jpg . (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round \"test statistic\" values to 2 decimal places and \"p-value\" to 4 decimal places.)
Test Statistic
p-value
a.
= 5,160; n = 115
2.49
0.0129
Reject H0
b.
= 5,160; n = 215
3.40
0.0007
Reject H0
c.
= 4,700; n = 42
-2.82
0.0048
Reject H0
d.
= 4,780; n = 42
-2.07
0.0388
Reject H0
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
5000
Level of Significance
0.1
Population Standard Deviation
690
Sample Size
115
Sample Mean
5160
Intermediate Calculations
Standard Error of the Mean
64.3428
Z Test Statistic
2.49
Two-Tail Test
Lower Critical Value
-1.6449
Upper Critical Value
1.6449
p-Value
0.0129
Reject the null hypothesis
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
5000
Level of Significance
0.1
Population Standard Deviation
690
Sample Size
215
Sample Mean
5160
Intermediate Calculations
Standard Error of the Mean
47.0576
Z Test Statistic
3.40
Two-Tail Test
Lower Critical Value
-1.6449
Upper Critical Value
1.6449
p-Value
0.0007
Reject the null hypothesis
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
5000
Level of Significance
0.1
Population Standard Deviation
690
Sample Size
42
Sample Mean
4700
Intermediate Calculations
Standard Error of the Mean
106.4693
Z Test Statistic
-2.82
Two-Tail Test
Lower Critical Value
-1.6449
Upper Critical Value
1.6449
p-Value
0.0048
Reject the null hypothesis
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
5000
Level of Significance
0.1
Population Standard Deviation
690
Sample Size
42
Sample Mean
4780
Intermediate Calculations
Standard Error of the Mean
106.4693
Z Test Statistic
-2.07
Two-Tail Test
Lower Critical Value
-1.6449
Upper Critical Value
1.6449
p-Value
0.0388
Reject the null hypothesis
| H0: = 5,000 |
| HA: 5,000 |
