Homework SourseInformation for Problems 34 Use the data stored that contain
Information for Problems 3-4: Use the data stored that contains resistor measurements from 2 different vendors.
Resistance measured in Ohms for 2 samples
Sample 1 - from Vendor A, 25 resistors
Sample 2 - from Vendor B, 35 resistors
Sample 1
Sample 2
96.8
106.8
99.4
103.2
97.7
102.6
99.6
104.0
100.0
104.6
99.9
106.4
98.6
106.8
101.2
103.7
100.3
100.3
101.1
106.3
101.9
103.5
98.2
106.8
98.5
104.7
103.7
106.8
101.0
104.0
98.6
102.2
98.3
106.3
97.7
104.1
99.4
104.7
98.2
105.1
99.7
107.0
99.8
102.8
99.6
109.2
101.1
107.1
99.1
108.0
104.0
104.3
104.2
107.2
107.7
102.2
106.2
105.8
103.4
105.4
3.)Conduct a hypothesis test at the a=0.10 level of significance to determine if the mean resistance of the resistors from vendor A (Sample 1) is less than 100 ohms. Assume this sample comes from a population with a normal distribution. Include all 5 steps. (5 points)
a.) State the null and alternative hypotheses.
b.)Calculate the test statistic. Be sure to state whether the test statistic is a z or a t score.
c.)Calculate the p-value.
d.)What is your decision?
e.)Interpret your conclusion in the context of this problem.
4.)Conduct a hypothesis test at the a=0.10 level of significance to determine if the mean resistance of the resistors from vendor B (Sample 2) is greater than 105 ohms. Assume this sample comes from a population with a normal distribution. Include all 5 steps. (5 points)
a.)State the null and alternative hypotheses.
b.)Calculate the test statistic. Be sure to state whether the test statistic is a z or a t score.
c.)Calculate the p-value.
d.)What is your decision?
c.)Interpret your conclusion in the context of this problem.
| Resistance measured in Ohms for 2 samples | ||
| Sample 1 - from Vendor A, 25 resistors | ||
| Sample 2 - from Vendor B, 35 resistors | ||
| Sample 1 | Sample 2 | |
| 96.8 | 106.8 | |
| 99.4 | 103.2 | |
| 97.7 | 102.6 | |
| 99.6 | 104.0 | |
| 100.0 | 104.6 | |
| 99.9 | 106.4 | |
| 98.6 | 106.8 | |
| 101.2 | 103.7 | |
| 100.3 | 100.3 | |
| 101.1 | 106.3 | |
| 101.9 | 103.5 | |
| 98.2 | 106.8 | |
| 98.5 | 104.7 | |
| 103.7 | 106.8 | |
| 101.0 | 104.0 | |
| 98.6 | 102.2 | |
| 98.3 | 106.3 | |
| 97.7 | 104.1 | |
| 99.4 | 104.7 | |
| 98.2 | 105.1 | |
| 99.7 | 107.0 | |
| 99.8 | 102.8 | |
| 99.6 | 109.2 | |
| 101.1 | 107.1 | |
| 99.1 | 108.0 | |
| 104.0 | ||
| 104.3 | ||
| 104.2 | ||
| 107.2 | ||
| 107.7 | ||
| 102.2 | ||
| 106.2 | ||
| 105.8 | ||
| 103.4 | ||
| 105.4 | ||
Solution
3.
a)
Formulating the null and alternative hypotheses,
Ho: u >= 100 [ANSWER]
Ha: u < 100 [ANSWER]
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b)
As we can see, this is a left tailed test.
df = n - 1 = 24
Getting the test statistic, as
X = sample mean = 99.576
uo = hypothesized mean = 100
n = sample size = 25
s = standard deviation = 1.528964791
Thus, t = (X - uo) * sqrt(n) / s = -1.386559071 [ANSWER, TEST STATISTIC]
***********************
C)
Also, the p value is, as df = 24,
p = 0.089161242 [ANSWER]
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d)
As P < 0.10, we REJECT THE NULL HYPOTHESIS.
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e)
There is significant evidence that the mean resistance of the resistors from vendor A is less than 100 ohms. [CONCLUSION]
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