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andre [41]
3 years ago
7

An article reported that for a sample of 58 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 164.55. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.) 611.81 , 696.51 ppm
Mathematics
1 answer:
Pavel [41]3 years ago
7 0

Answer:

95% Confidence Interval = (611.81 ppm, 696.51 ppm)

Step-by-step explanation:

The formula for Confidence Interval is given as:

Confidence Interval = Mean ± z × s /√n

Mean = the sample mean/average = 654.16

s = the sample standard deviation = 164.55

z = z score of 95% confidence interval = 1.96

Confidence Interval =

654.16 ± 1.96 × 164.55/√58

= 654.16 ± 42.348

Hence,

654.16 - 42.348

= 611.812

Approximately to two decimal places = 611.81 ppm

654.16 + 42.348

= 696.508

Approximately to two decimal places = 696.51 ppm

Therefore, the 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected is (611.81 ppm, 696.51 ppm).

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By utilizing the law of the sines and Heron's formula, we find that the <em>approximate</em> area of the triangle is approximately 73.1 square centimeters. (Correct choice: A)

<h3>How to calculate the area of a triangle by Heron's formula</h3>

Prior to using Heron's formula, we must find the lengths of the missing sides by law of the sines:

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