You have these questions on your website, and you have the answer for 95%, please compute a 98% confidence interval. Only compute a 98% confidence interval.Cost to Repair Fire Damage, The mean cost to repair the smoke and fire damage that results from home fires of all causes is $11,389 (HomeAdvisor). How does the damage that results from home fires caused by careless use of tobacco compare? The file TobaccoFires provides the cost to repair smoke and fire damage associated with a sample of 55 fires caused by careless use of tobacco products. Using past years’ data, the population standard deviation can be assumed known with cr = $3027. What is the 95% confidence interval estimate of the mean cost to repair smoke and fire damage that results from home fires caused by careless use of tobacco? compute also a 98% confidence interval. Smoke and Fire CostMean19100Standard Error406.209178Median19042Mode#N/AStandard Deviation3012.527891Sample Variance9075324.296Kurtosis-1.073940579Skewness-0.146473098Range10381Minimum13561Мaximum23942Sum1050500Count55From the output, the mean value is 19,100 and the number of taxesis 55.The formula of confidence interval for population mean is asfollows:From "Table 8.1 value of zg ", the value of :for the 95%confidence interval is 1.96.The value of confidence interval for population mean is as follows:3,02719, 100 ± 1.96-V5519, 100 + (1.96х 407.95)= 19, 100 ± 799.582= (19, 100 – 800, 19, 100 + 800)= (18, 300, 19,900) Expert SolutionTo determineFind the 95% confidence interval for the mean cost of repairingsmoke and fire damages due to careless use of tobacco.Compare the mean cost to repair the smoke with fire damages ofhomes in all the cases.Answer to Problem 9EThe 95% confidence interval for the mean cost of repairing smokeand fire damages due to careless use of tobacco is (18, 300, 19,900).Explanation of SolutionCalculation:The given information is that the average cost to repair the smokeand fire damages from home fires in any cause is $11,389. Thesample of 55 fires caused the careless use of tobacco products. Thepopulation standard deviation is $3,027.Software Procedure:Step-by-step procedure to obtain the mean value using Excel:• In Excel sheet, enter Smoke and Fire Cost in one column.In Data, select Data Analysis and choose DescriptiveStatistics.• In Input Range, select Variable and click Labels in First Row.• Select Summary Statistics.• Click Ok.Output using Excel is given below:

Given Mean X¯=19100 Standard deviation σ=3027. The 98% confidence interval is determined using the formula CI=X¯+zα/2σn. The z value for 98% confidence interval is 2.326. Substitute the respective values in the equation. CI=19100±2.326302755=19100±949.38=20049.38,18150.62Therefore the 98% confidence interval estimates of the mean cost to repair smoke and fire damage that result from home fire caused by careless use of tobacco is 18150.62,20049.38.

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A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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You have these questions on your website, and you have the answer for 95%, please compute a 98% confidence interval. Only compute a 98% confidence interval.

Cost to Repair Fire Damage, The mean cost to repair the smoke and fire damage that results from home fires of all causes is $11,389 (HomeAdvisor). How does the damage that results from home fires caused by careless use of tobacco compare? The file TobaccoFires provides the cost to repair smoke and fire damage associated with a sample of 55 fires caused by careless use of tobacco products. Using past years’ data, the population standard deviation can be assumed known with cr = $3027. What is the 95% confidence interval estimate of the mean cost to repair smoke and fire damage that results from home fires caused by careless use of tobacco? compute also a 98% confidence interval.

Smoke and Fire Cost
Mean
19100
Standard Error
406.209178
Median
19042
Mode
#N/A
Standard Deviation
3012.527891
Sample Variance
9075324.296
Kurtosis
-1.073940579
Skewness
-0.146473098
Range
10381
Minimum
13561
Мaximum
23942
Sum
1050500
Count
55
From the output, the mean value is 19,100 and the number of taxes
is 55.
The formula of confidence interval for population mean is as
follows:
From "Table 8.1 value of zg ", the value of :
for the 95%
confidence interval is 1.96.
The value of confidence interval for population mean is as follows:
3,027
19, 100 ± 1.96-
V55
19, 100 + (1.96х 407.95)
= 19, 100 ± 799.582
= (19, 100 – 800, 19, 100 + 800)
= (18, 300, 19,900)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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