The National Association of Home Builders provided data on the cost of the two m

Question

The National Association of Home Builders provided data on the cost of the two most popular home remodeling projects. Sample data on cost in thousands of dollars for two types of remodeling projects are as follows Kitchen Kitchen 27.0 17.4 22.8 21.9 21.0 Master Bedroom 18.0 21.1 26.4 24.8 25.4 23.0 19.7 16.9 21.8 19.0 Master Bedroom 17.8 24.6 22.0 a. Using Kitchen as population 1 and Master Bedroom as population 2, develop a point estimate of the difference between the population mean remodeling costs for the two types of projects (to 1 decimal) 1.4 thousand b. Develop a 90% confidence interval for the difference between the two population means (to 1 decimal). Use z-table

Explanation / Answer

a. Here point estimate of the difference between the population mean remodeling costs for two type of projects.

Herre point estimate = x2 - x1 = 22.5125 - 21.05 = $ 1.4625 (in thousand) or 1.5 (inthousand)

(b) 90% confidence interval

Here we have to use the Z table  

Z value = +-1.645

Confidence interval = (x2- x1) +- Z * sqrt [12 /n1 + 22 /n2]

Here we are using Z table that'why standard deviation of samples are taken as standard deviation of population.

12 = 8.9028

22 = 11.1241

Lower control limit = 1.4625 - 1.645 * sqrt [8.9028/10 + 11.1234/8] = - 1.02178 (in thousands)

Upper COntrol Limit = 1.4625 + 1.645 * sqrt [8.9028/10 + 11.1234/8] = 3.9468 (in thousndas)

in one decimal

(-1.0, 3.9)

Kitchen master Bedroom 27.0 18 17.4 21.1 22.8 26.4 21.9 24.8 21.0 25.4 23.0 17.8 19.7 24.6 16.9 22 21.8 19.0 Average 21.05 22.5125

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