16/05/2014

Quiz 4

1. (8-28) (18 points) An Izod impact test was performed on 20 specimens of PVC pipe. Assume that the population is normally distributed. The sample mean is ̅ and the sample standard deviation is

. Find a 99% lower confidence bound on Izod impact strength.

Sol: 99% lower confidence bound on mean Izod impact strength n 20 x 1.25 s 0.25

t0.01,19 2.539

s x t0.01,19

n

0.25

1.25 2.539

20

1.108

2. (28-5) (18 points) A random sample of 100 automobile owners shaws that, in the state of

Virginia, an automobile is driven on the average 23500 kilometers per year with a standard deviation of 3900 kilometers. Construct a 99% confidence interval for the average number of kilometers an automobile is driven annually in Virginia.

Sol: 99% confidence interval, z distribution can be used

N=100 ̅

̅

̅

√

√

3. (9-58) An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 59–75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59.

a. (11 points)Test the hypotheses versus , using

.

b. (11 points) Compute the power of the test if the true mean interior temperature is as high as 22.75.

9-54

Sol: a)

1) The parameter of interest is the true mean interior temperature life, .

2) H0 : = 22.5

3) H1 : 22.5

4) t0

x s/ n

5) Reject H0 if |t0| > t/2,n-1 where = 0.05 and t/2,n-1 = 2.776 for n = 5

6) x 22.496 , s = 0.378, n = 5 t0

22.496 22.5

0.378 / 5

0.00237

7) Because –0.00237 > 2.776 we cannot reject the null hypothesis. There is not sufficient evidence to conclude that the true mean interior temperature is not equal to 22.5C at = 0.05.

b) d =

| 0 | | 22.75 22.5 |