Question

An article reported that for a sample of 48 kitchens with gas cooking appliances monitored during a one-week period, the sample mean co2 level (ppm) was 654.16, and the sample standard deviation was 165.91.

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.)
____X_____ ppm

Interpret the resulting interval.
a.We are 95% confident that the true population mean lies below this interval.
b.We are 95% confident that this interval contains the true population mean.
c.We are 95% confident that this interval does not contain the true population mean.
d.We are 95% confident that the true population mean lies above this interval.

Answer 1

To calculate the 95% confidence interval for the true average CO2 level in the population of all homes, we use the formula CI = X ± Z * (σ/√n), where X is the sample mean, Z is the Z-score corresponding to the desired confidence level, σ is the sample standard deviation, and n is the sample size. Using the given values, the 95% confidence interval for the true average CO2 level is (606.17, 702.15). The correct option is b.

Step-by-step explanation:

To calculate the 95% confidence interval for the true average CO2 level in the population of all homes, we will use the formula:

CI = X ± Z * (σ/√n)

Where:

• CI is the confidence interval

• X is the sample mean

• Z is the Z-score corresponding to the desired confidence level

• σ is the sample standard deviation

• n is the sample size

In this case, the sample mean (X) is 654.16, the sample standard deviation (σ) is 165.91, and the sample size (n) is 48. The Z-score corresponding to a 95% confidence level is 1.96.

Plugging in the values:

CI = 654.16 ± 1.96 * (165.91/√48) = 654.16 ± 47.99

So, the 95% confidence interval for the true average CO2 level is (606.17, 702.15).

The correct option is b. We are 95% confident that this interval contains the true population mean.