In: Statistics and Probability
Recall that a bank manager has developed a new system to reduce
the time customers spend...
- Recall that a bank manager has developed a new system to reduce
the time customers spend waiting for teller service during peak
hours. The manager hopes the new system will reduce waiting times
from the current 9 to 10 minutes to less than 6 minutes.
Suppose the manager wishes to use the
random sample of 100 waiting times to support the claim that the
mean waiting time under the new system is shorter than six
minutes.
- Letting μ represent the mean waiting time under the new system,
set up the null and alternative hypotheses needed if we wish to
attempt to provide evidence supporting the claim that μ is shorter
than six minutes.
- The random sample of 100 waiting times yields a sample mean of
5.46 minutes. Assuming that the population standard
deviation equals 2.47 minutes, use critical values to test
H0 versus Ha at each of α =
.10, .05, .01, and .001.
- Using the information in part b, calculate the
p-value and use it to test H0 versus
Ha at each of α = .10, .05, .01, and .001.
- How much evidence is there that the new system has reduced the
mean waiting time to below six minutes?