(a) A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected and the amount of gas (therms) used during the month of January is determined for each house. The resulting observations are 122, 109, 145, 103, 138, 147, 87, 125, 118, 99. Let u denote the average gas usage during January by all houses in this area. Compute a point estimate of u. therms (b) Suppose there are 24,000 houses in this area that use natural gas for heating. Let r denote the total amount of gas used by all of these houses during January. Estimate T using the data of part (a). therms What estimator did you use in computing your estimate? (c) Use the data in part (a) to estimate p. the proportion of all houses that used at least 100 therms. (d) Give a point estimate of the population median usage (the middle value in the population of all houses) based on the sample of part (a). therms What estimator did you use? O s/x IN IX
(a) A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected and the amount of gas (therms) used during the month of January is determined for each house. The resulting observations are 122, 109, 145, 103, 138, 147, 87, 125, 118, 99. Let u denote the average gas usage during January by all houses in this area. Compute a point estimate of u. therms (b) Suppose there are 24,000 houses in this area that use natural gas for heating. Let r denote the total amount of gas used by all of these houses during January. Estimate T using the data of part (a). therms What estimator did you use in computing your estimate? (c) Use the data in part (a) to estimate p. the proportion of all houses that used at least 100 therms. (d) Give a point estimate of the population median usage (the middle value in the population of all houses) based on the sample of part (a). therms What estimator did you use? O s/x IN IX
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Educational Website Content: Gas Usage Estimation**
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### Problem Statement
**(a)** A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected. The amount of gas (therms) used during the month of January is determined for each house. The resulting observations are:
- 122, 109, 145, 103, 138, 147, 87, 125, 118, 99
Let \( \mu \) denote the average gas usage during January by all houses in this area. Compute a point estimate of \( \mu \).
\[ \text{Estimated } \mu: \boxed{} \text{ therms} \]
**(b)** Suppose there are 24,000 houses in this area that use natural gas for heating. Let \( \tau \) denote the total amount of gas used by all of these houses during January. Estimate \( \tau \) using the data from part (a).
\[ \tau: \boxed{} \text{ therms} \]
**What estimator did you use in computing your estimate?**
- \( \circ \) \( \bar{x} \)
- \( \circ \) \( \hat{\beta} \)
- \( \circ \) \( s/\sqrt{n} \)
- \( \bullet \) \( \sum x \) (Selected)
**(c)** **Use the data in part (a) to estimate \( p \), the proportion of all houses that used at least 100 therms.**
\[ p: \boxed{} \]
**(d)** **Give a point estimate of the population median usage (the middle value in the population of all houses) based on the sample from part (a).**
\[ \text{Median:} \boxed{} \text{ therms} \]
**What estimator did you use?**
- \( \circ \) \( s \)
- \( \circ \) \( \bar{x} \)
- \( \circ \) \( \hat{\beta} \)
- \( \bullet \) Median (Selected)
---
### Explanation
#### Observations:
The data consists of gas usage (in therms) from a sample of 10 houses.
#### Estimators:
- **\( \bar{x} \)** is the sample mean, used to estimate the population mean.
- **Median** is the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcdbb6667-2d1e-4df4-b920-eeb3e502e5d9%2F963e0569-dbbb-4ef7-b17a-05f66711987a%2Fmghwvf_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Content: Gas Usage Estimation**
---
### Problem Statement
**(a)** A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected. The amount of gas (therms) used during the month of January is determined for each house. The resulting observations are:
- 122, 109, 145, 103, 138, 147, 87, 125, 118, 99
Let \( \mu \) denote the average gas usage during January by all houses in this area. Compute a point estimate of \( \mu \).
\[ \text{Estimated } \mu: \boxed{} \text{ therms} \]
**(b)** Suppose there are 24,000 houses in this area that use natural gas for heating. Let \( \tau \) denote the total amount of gas used by all of these houses during January. Estimate \( \tau \) using the data from part (a).
\[ \tau: \boxed{} \text{ therms} \]
**What estimator did you use in computing your estimate?**
- \( \circ \) \( \bar{x} \)
- \( \circ \) \( \hat{\beta} \)
- \( \circ \) \( s/\sqrt{n} \)
- \( \bullet \) \( \sum x \) (Selected)
**(c)** **Use the data in part (a) to estimate \( p \), the proportion of all houses that used at least 100 therms.**
\[ p: \boxed{} \]
**(d)** **Give a point estimate of the population median usage (the middle value in the population of all houses) based on the sample from part (a).**
\[ \text{Median:} \boxed{} \text{ therms} \]
**What estimator did you use?**
- \( \circ \) \( s \)
- \( \circ \) \( \bar{x} \)
- \( \circ \) \( \hat{\beta} \)
- \( \bullet \) Median (Selected)
---
### Explanation
#### Observations:
The data consists of gas usage (in therms) from a sample of 10 houses.
#### Estimators:
- **\( \bar{x} \)** is the sample mean, used to estimate the population mean.
- **Median** is the
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