MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Confidence Interval Computation Tool

#### Inputs:
- **Sample size:**
- **Point estimate:**
- **Population standard deviation:**
- **Critical value:**

Click the "Compute" button to calculate:

- **Standard error:**
- **Margin of error:**
- **95% confidence interval:**

#### Confidence Level Table:
| Confidence level | Critical value |
|------------------|----------------|
| 99%              | 2.576          |
| 95%              | 1.960          |
| 90%              | 1.645          |

#### Exercise:
(b) Based on your sample, enter the lower and upper limits to graph the 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model.

#### Graph:
- **95% Confidence Interval Slider:**
  - Displays a draggable line which represents the range for the confidence interval.
  - The scale is from 0.00 to 10.00, allowing you to adjust the lower and upper bounds.

This tool assists in visualizing and calculating confidence intervals for statistical analysis in determining population parameters.
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Transcribed Image Text:### Confidence Interval Computation Tool #### Inputs: - **Sample size:** - **Point estimate:** - **Population standard deviation:** - **Critical value:** Click the "Compute" button to calculate: - **Standard error:** - **Margin of error:** - **95% confidence interval:** #### Confidence Level Table: | Confidence level | Critical value | |------------------|----------------| | 99% | 2.576 | | 95% | 1.960 | | 90% | 1.645 | #### Exercise: (b) Based on your sample, enter the lower and upper limits to graph the 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. #### Graph: - **95% Confidence Interval Slider:** - Displays a draggable line which represents the range for the confidence interval. - The scale is from 0.00 to 10.00, allowing you to adjust the lower and upper bounds. This tool assists in visualizing and calculating confidence intervals for statistical analysis in determining population parameters.
### Estimating the Population Mean of Battery Lifetimes

A cell phone manufacturer has hired you to estimate the population mean of the battery lifetimes for all phones of their latest model. Battery lifetime is measured as the time it takes for the battery charge to run out while a tester streams videos on the phones continuously. A random sample of 45 cell phones of the latest model is selected, and their battery lifetimes are recorded. The population standard deviation of the battery lifetimes for this model is assumed to be 2.42 hours.

#### Task

Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. (If necessary, consult a list of formulas.)

#### Instructions

1. **Click on "Take Sample"** to see the results from your random sample of 45 phones of the manufacturer's latest model.

   ![Diagram of Sample Data](diagram-placeholder)

   **Table: Sample Data**
   | Number of phones | Sample mean | Sample standard deviation | Population standard deviation |
   |------------------|-------------|---------------------------|-------------------------------|
   | 45               | 5.49        | 2.15                      | 2.42                          |

2. **Enter the following values:**
   - **Sample size**
   - **Point estimate for the population mean**
   - **Population standard deviation**
   - **Critical value for your 95% confidence interval** (Choose from the provided table of critical values.)

3. **Compute the Results:**
   - Enter the values in the provided fields for sample size, point estimate, population standard deviation, and critical value.
   - Then, click "Compute" to calculate the standard error and construct the confidence interval.

**Note:** Ensure you follow the instructions and input the relevant values accurately to determine the correct confidence interval.
expand button
Transcribed Image Text:### Estimating the Population Mean of Battery Lifetimes A cell phone manufacturer has hired you to estimate the population mean of the battery lifetimes for all phones of their latest model. Battery lifetime is measured as the time it takes for the battery charge to run out while a tester streams videos on the phones continuously. A random sample of 45 cell phones of the latest model is selected, and their battery lifetimes are recorded. The population standard deviation of the battery lifetimes for this model is assumed to be 2.42 hours. #### Task Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the battery lifetimes for all phones of the manufacturer's latest model. (If necessary, consult a list of formulas.) #### Instructions 1. **Click on "Take Sample"** to see the results from your random sample of 45 phones of the manufacturer's latest model. ![Diagram of Sample Data](diagram-placeholder) **Table: Sample Data** | Number of phones | Sample mean | Sample standard deviation | Population standard deviation | |------------------|-------------|---------------------------|-------------------------------| | 45 | 5.49 | 2.15 | 2.42 | 2. **Enter the following values:** - **Sample size** - **Point estimate for the population mean** - **Population standard deviation** - **Critical value for your 95% confidence interval** (Choose from the provided table of critical values.) 3. **Compute the Results:** - Enter the values in the provided fields for sample size, point estimate, population standard deviation, and critical value. - Then, click "Compute" to calculate the standard error and construct the confidence interval. **Note:** Ensure you follow the instructions and input the relevant values accurately to determine the correct confidence interval.
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