1 The maximum acceptable level for exposure to microwave rad

1. The maximum acceptable level for exposure to microwave radiation is 10
W=cm2. It is feared that a large television transmitter is polluting a region
nearby. A sample of 25 readings is selected at random over a one-week period
with a sample mean of X
= 10:3 and sample variance of s2 = 4.
(a) Calculate the 95% confidence interval for the mean output of the power
supplies.
(b) Based on your results above would you reject the null hypothesis that the
microwave radiation is at an acceptable level?
2. A small computer network consists of ten users and one printer. The average
turn around time for the system is 15 minutes. Ten new users and a second
printer are added to the system. A sample of 30 turnaround times for the new
network yields an average turnaround time of X
= 14 and a sample variance
of s2 = 9.
(a) Calculate the 95% confidence interval for the mean turnaround time.
(b) Is there evidence to support the assertion that the modifications to the
system have had no effect on turnaround times?
3. We want to estimate the mean capacitance for a set of capacitors. The nominal
rating for the units is 9 F. A sample of 10 units finds that the sample mean
and variance are X
= 9:4 F and s2 = 0:53 F2.
(a) Calculate the 95% confidence interval for the mean capacitance of these
capacitors.
(b) Based on your results above would you reject the null hypothesis H0 :
= 9?
(c) Now consider that you collected identical measurements for X
and s2 but
from a sample size of 20. Are your results the same as in part b. If not
why?

Solution

a)The 95% confidence interval for means is:

M plus minus t24,0.05*(s/root over n)

=10.3 plus minus 2.064*(2/5)

=10.3 plus minus 0.8256

=(9.4744,11.1256)

b)The confidence interval contains the true population mean thus can not reject the null hypothesis.