### Statistical Analysis of CO₂ Levels in Kitchens with Gas AppliancesAn article reported data for a sample of 54 kitchens with gas cooking appliances. Over a one-week monitoring period, the sample mean CO₂ level was 654.16 ppm, and the sample standard deviation was 163.36 ppm.#### (a) Confidence Interval CalculationCalculate and interpret a 95% confidence interval for the true average CO₂ level in the population of all homes with gas appliances.- **Confidence Interval Formula**: \[ \left(631.92, \text{upper limit value to be calculated}\right) \text{ ppm} \]- **Interpretation of the Interval**: - **Selected Option**: "We are 95% confident that this interval contains the true population mean." This means that if we were to take many samples and build a confidence interval from each, approximately 95% of those intervals would contain the true population mean CO₂ level.#### (b) Sample Size DeterminationSuppose the investigators estimated the standard deviation (\(s\)) as 172 ppm before data collection. Determine the necessary sample size to obtain an interval width of 51 ppm for a 95% confidence level.- **Solution Format**: - Required sample size: \([ \text{Calculated Number} ]\) kitchensThis step involves using a standard formula for sample size calculation to ensure the desired precision of the interval width at the specified confidence level.

The sample size is 54, the sample mean is 654.16 and the sample standard deviation is 163.36.

Answered: An article reported that for a sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of T = 74 hours. The population standard deviation is known to be 5.8 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.5 hours at a 90% level of confidence. How many more bacteria should you sample to achieve a 0.5 hour margin of error? n bacteria %3D
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According to the World Health Organization, the average height of a one-year-old child is 29". You believe children with a particular disease are smaller than average, so you draw a sample of 20 children with this disease and find a mean height of 27.5" and a sample standard deviation of 1.5". The test statistic is -4.4721 and the p-value is 0.00013 using the calculator function TTEST. If a=0.05, what conclusions can be made? Provide a detailed conclusion including contextualization to the given scenario.
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You suspect that people living in urban areas produce on average more garbage (X)than those living in rural areas (Y). To verify this opinion, you draw two samples and collect information on the amount of garbage produced in a month (measured in kilos). The first sample, made of 8 subjects living in an urban area, provides a sample mean equal to 40.5 and a sample standard deviation equal to 5.6; in the second sample, made of 10 subjects living in rural areas, the sample mean is 35.6 and the sample standard deviation is 7.5. It is assumed that the two populations are normal with the same unknown variance.Test the null hypothesis that the two population means are equal against a one-sided alternative according to which people living in urban areas produce on average more garbage than those living in rural areas. Use a 1% significance level.
webassign.net The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.32 A, with a sample standard deviation of s = 0.43 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.) What are we testing in this problem? O single proportion O single mean (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H # 0.8; H1: µµ = 0.8 Ο H0: μ = 0.8; H1: μ+ 0.8 O Ho: p = 0.8; H1: p > 0.8 O Ho: p + 0.8; H1: p = 0.8 O Ho: p = 0.8; H1: p + 0.8 O Ho: H = 0.8; H1: µ > 0.8 (b) What sampling distribution will you use? What assumptions are you making? O The Student's t, since we assume that x has a normal distribution with known o. O The standard normal, since we assume that x has a normal distribution with known ơ. O The Student's t, since we assume that x has a normal…
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