Please solve the screenshot, thanks!! The answers are not (604.52, 703.80) for (a) nor 45 for (b). ### Understanding Confidence Intervals in Real-World MeasurementsAn article reported data from a study on gas cooking appliances in 45 different kitchens. In this study, the carbon dioxide (CO2) levels were monitored over one week. Here, we'll walk through calculating and interpreting a 95% confidence interval for the true average CO2 level in the population.#### Study Details:- **Sample size (n):** 45 kitchens- **Sample Mean CO2 level:** 654.16 ppm- **Sample Standard Deviation (s):** 165.23 ppm### Step-by-Step Calculation:#### (a) Calculate and interpret a 95% confidence interval for the true average CO2 level:- **Formula Used:** The confidence interval can be calculated using the formula: \[ \bar{x} \pm t^* \left(\frac{s}{\sqrt{n}}\right) \] Where: - $ \bar{x} $ = sample mean - $ t^* $ = t-multiplier from the t-distribution for 95% confidence - $ s $ = sample standard deviation - $ n $ = sample size- **Determine the Interval:** - Enter values in the provided fields as calculated. - Round answers to two decimal places.##### **Interpretation:**- Select the statement: "We are 95% confident that this interval contains the true population mean."- This means if we were to take many samples and create intervals, 95% would contain the true population mean.#### (b) Considering Sample Size:- **Scenario:** If investigators guessed $ s = 177 $ before data collection,- **Goal:** Determine sample size for an interval width of 52 ppm at 95% confidence.- **Calculation Tip:** Use the formula involving desired width to find the necessary sample size.**Input:** - Fill in the box with the calculated number of kitchens needed.This educational exercise exemplifies how statistical methods can help us estimate averages and make informed decisions based on data.

Given: Let 'n' represents the size of the sample; that is; n=45. Let X¯ represents the sample mean…

An article reported that for a sample of 45 kitchens with gas cooking appliances monitored during a one-week period, the sample mean Co, level (ppm) was 654.16, and the sample standard deviation was 165.23. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average co, level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.) ) ppm Interpret the resulting interval. O we are 95% confident that the true population mean lies below this interval. O we are 95% confident that this interval does not contain the true population mean. O we are 95% confident that the true population mean lies above this interval. O we are 95% confident that this interval contains the true population mean. (b) Suppose the investigators had made a rough guess of 177 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 52 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.) kitchens

An article reported that for a sample of 45 kitchens with gas cooking appliances monitored during a one-week period, the sample mean Co, level (ppm) was 654.16, and the sample standard deviation was 165.23. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average co, level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.) ) ppm Interpret the resulting interval. O we are 95% confident that the true population mean lies below this interval. O we are 95% confident that this interval does not contain the true population mean. O we are 95% confident that the true population mean lies above this interval. O we are 95% confident that this interval contains the true population mean. (b) Suppose the investigators had made a rough guess of 177 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 52 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.) kitchens

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 14CR

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Please solve the screenshot, thanks!! The answers are not (604.52, 703.80) for (a) nor 45 for (b).

### Understanding Confidence Intervals in Real-World Measurements

An article reported data from a study on gas cooking appliances in 45 different kitchens. In this study, the carbon dioxide (CO2) levels were monitored over one week. Here, we'll walk through calculating and interpreting a 95% confidence interval for the true average CO2 level in the population.

#### Study Details:

- **Sample size (n):** 45 kitchens
- **Sample Mean CO2 level:** 654.16 ppm
- **Sample Standard Deviation (s):** 165.23 ppm

### Step-by-Step Calculation:

#### (a) Calculate and interpret a 95% confidence interval for the true average CO2 level:

- **Formula Used:** The confidence interval can be calculated using the formula:

\[ \bar{x} \pm t^* \left(\frac{s}{\sqrt{n}}\right) \]

Where:
- $ \bar{x} $ = sample mean
- $ t^* $ = t-multiplier from the t-distribution for 95% confidence
- $ s $ = sample standard deviation
- $ n $ = sample size

- **Determine the Interval:**
- Enter values in the provided fields as calculated.
- Round answers to two decimal places.

##### **Interpretation:**

- Select the statement: "We are 95% confident that this interval contains the true population mean."
- This means if we were to take many samples and create intervals, 95% would contain the true population mean.

#### (b) Considering Sample Size:

- **Scenario:** If investigators guessed $ s = 177 $ before data collection,
- **Goal:** Determine sample size for an interval width of 52 ppm at 95% confidence.

- **Calculation Tip:** Use the formula involving desired width to find the necessary sample size.

**Input:**
- Fill in the box with the calculated number of kitchens needed.

This educational exercise exemplifies how statistical methods can help us estimate averages and make informed decisions based on data.

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