math 112
STAT 208
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 |
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 |