How well materials conduct heat matters when designing houses, for example. Cond

Question

How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institute of Standards and Technology provides exact data on properties of materials. Here are 11 measurements of the heat conductivity of a particular type of glass:

The mean (±0.001) and the standard deviation (±0.0001) of the SRS are:   
x¯ = ? s = ?

The critical value (±0.001) from the distribution for 90% confidence interval is:   
t* = ___?

The 90% confidence interval (±0.001) for the mean conductivity is
from _____ to ____ .

Is there significant evidence at the 10% level that the mean conductivity of this type of glass is not 1?

No

Yes

Conductivity   1.1 1.27 1.2 1.27 0.92 1.05 1.12 1.35 1.35 0.99 0.92

Explanation / Answer

How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institute of Standards and Technology provides exact data on properties of materials. Here are 11 measurements of the heat conductivity of a particular type of glass:

Conductivity  

1.1

1.27

1.2

1.27

0.92

1.05

1.12

1.35

1.35

0.99

0.92

The mean (±0.001) and the standard deviation (±0.0001) of the SRS are:   
x¯ = 1.140 s = 0.160

The critical value (±0.001) from the distribution for 90% confidence interval is:   
t* = 1.812

The 90% confidence interval (±0.001) for the mean conductivity is
from 1.053 to 1.227 .

Is there significant evidence at the 10% level that the mean conductivity of this type of glass is not 1?

No

Yes

Answer : yes

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

0.160

Sample Mean

1.140

Sample Size

11.000

Confidence Level

0.900

Intermediate Calculations

Standard Error of the Mean

0.048

Degrees of Freedom

10.000

t Value

1.812

Interval Half Width

0.087

Confidence Interval

Interval Lower Limit

1.053

Interval Upper Limit

1.227

Conductivity  

1.1

1.27

1.2

1.27

0.92

1.05

1.12

1.35

1.35

0.99

0.92

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