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 the properties of materials. Here are 11 measurements of the heat conductivity of a particular type of glass.

1.10    1.06    1.12    1.07    1.13    1.07    1.09    1.16    1.16    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 a 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 90% confidence interval for the mean conductivity. (Use 3 decimal places.)
(?, ?)

2.

In a sample of 53 randomly selected students, 34 favored the amount being budgeted for next year's intramural and interscholastic sports. Construct a 90% confidence interval for the proportion of all students who support the proposed budget amount. (Give your answers correct to three decimal places.)

Lower Limit
Upper Limit

Answer 1

sems	leaves
1.0	NONE
1.0	6779
1.1	0233
1.1	668

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

b)

sample mean 'x̄=		1.115
sample size    n=		11
std deviation s=		0.0408
std error ='sx=s/√n=0.0408/√11=		0.0123

for 90% CI; and 10 df, value of t=		1.812		from excel: t.inv(0.95,10)
margin of error E=t*std error    =		0.022
lower bound=sample mean-E =		1.093
Upper bound=sample mean+E =		1.138
from above 90% confidence interval for population mean =(1.093<μ<1.138)

2)

sample success x =		34
sample size n=		53
pt estiamte p̂ =x/n=		0.6415
se= √(p*(1-p)/n) =		0.0659

for 90 % CI value of z=

1.645

from excel:normsinv((1+0.9)/2)

margin of error E=z*std error   =		0.1084
lower bound=p̂ -E                       =		0.533
Upper bound=p̂ +E                     =		0.750