To find:The 95% confidence interval for the population mean or population proportion and to interpret the confidence interval in context.
The 95% confidence interval for the population mean is
The confidence interval means that with a probability of 95% the battery life of the batteries would lie between 67.5 and 73.5 hours (approximately)
Given information:
Given, a consumer research group tested the battery life of 36 randomly chosen batteries to establish the likely battery life for the population of same type of battery as follows:
Calculation:
The mean of the data is given by:
To determine the variance, the following table is used:
63.2 | 70.5 | -7.3 | 53.3 |
62.1 | 70.5 | -8.4 | 70.6 |
79.4 | 70.5 | 8.9 | 79.2 |
66.3 | 70.5 | -4.2 | 17.6 |
61.2 | 70.5 | -9.3 | 86.5 |
61.4 | 70.5 | -9.1 | 82.8 |
68.3 | 70.5 | -2.2 | 4.8 |
86.2 | 70.5 | 15.7 | 246.5 |
71.4 | 70.5 | 0.9 | 0.8 |
84.6 | 70.5 | 14.1 | 198.8 |
81.8 | 70.5 | 11.3 | 127.7 |
75.2 | 70.5 | 4.7 | 22.1 |
74.5 | 70.5 | 4 | 16 |
74.5 | 70.5 | 4 | 16 |
83.6 | 70.5 | 13.1 | 171.6 |
82.2 | 70.5 | 11.7 | 136.9 |
64.3 | 70.5 | -6.2 | 38.4 |
63.6 | 70.5 | -6.9 | 47.6 |
78.4 | 70.5 | 7.9 | 62.4 |
63.6 | 70.5 | -6.9 | 47.6 |
54.1 | 70.5 | -16.4 | 269 |
71.6 | 70.5 | 1.1 | 1.2 |
72.4 | 70.5 | 1.9 | 3.6 |
75.6 | 70.5 | 5.1 | 26 |
59.3 | 70.5 | -11.2 | 125.4 |
72.7 | 70.5 | 2.2 | 4.8 |
59.6 | 70.5 | -10.9 | 118.8 |
85.8 | 70.5 | 15.3 | 234.1 |
64.2 | 70.5 | -6.3 | 39.7 |
73.4 | 70.5 | 2.9 | 8.4 |
60.1 | 70.5 | -10.4 | 108.2 |
81.3 | 70.5 | 10.8 | 116.6 |
74.1 | 70.5 | 3.6 | 13 |
47.6 | 70.5 | -22.9 | 524.4 |
71.8 | 70.5 | 1.3 | 1.7 |
68.1 | 70.5 | -2.4 | 5.8 |
Sum: | 3127.9 |
Hence,
The standard deviation is given by:
The margin of error at 95% confidence level is given by:
Here,
Plugging the values:
The confidence interval for a population mean at 95% confidence level is given by:
Here,
Plugging the values:
The confidence interval means that the battery life of 95% of the batteries would lie between 67.5 and 73.5 hours (approximately)
Conclusion:
The 95% confidence interval for the population meanis
The confidence interval means that with a probability of 95% the battery lifeof the batteries would lie between 67.5 and 73.5 hours (approximately)
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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