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 Institution 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.

1.11 1.05 1.12 1.07 1.13 1.07 1.08 1.15 1.17 1.18 1.13

(a) We can consider this an SRS of all specimens of glass of this type. Make a stemplot. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

Stems Leaves

1.0 1.0 1.1 1.1

Is there any sign of major deviation from Normality?

The stemplot shows that the data are not skewed and have no outliers.

The stemplot shows that the data is skewed to the left with one outlier.

The stemplot shows that the data is skewed to the right with one outlier.

(b) Give a 80% confidence interval for the mean conductivity. (Use 3 decimal places.)

(__________ , __________)

Answer 1

a)

Stems Leaves

1.0 5

1.0 7 7 8

1.1 1 2 3 3 5

1.1 7 8

The stem plot shows that the data is skewed to the left with one outlier.

b) The formula of lower and upper limit of the t confidence interval for population mean ( ) is as

Lower limit = - E

Lower limit = + E

Let's first find sample mean ( ),  sample standard deviation(s) and critical t value ( t_c ) using excel:

The formulae used on the above excel-sheet are as

Plug the values in the formula of E, we get:

Lower limit = - E = 1.1145 - 0.0178 = 1.0911 = 1.0968 = 1.097

Lower limit = + E = 1.1145 + 0.0178 = 1.132

The 80% confidence interval for the mean conductivity. (Use 3 decimal places.)

( 1.097, 1.132)