Question

4. A bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes that the new system will reduce waiting times from the current 9 to 10 minutes to less than 6 minutes. a. Set up the null and alternative hypotheses needed if we wish to attempt to provide evidence supporting the claim that the mean waiting time is shorter than six minutes. b. The mean and the standard deviation of a sample of 100 bank customer waiting times are 5.46 minutes and 2.475 minutes, respectively. (1) Use the critical value approach to test H0 versus Ha when α = 0.05. (2) Use the p-value approach to test H0 versus Ha when α = 0.05.

Answer 1

a)

H0: >= 6

Ha: < 6

b-1)

test statistics

t = - / S / sqrt(n)

= 5.46 - 6 / 2.475 / sqr(100)

= -2.18

This is test statistics value.

From T table,

Critical value at 0.05 level with 99 df = -1.660

Since test statistics < -1.660 , we have sufficient evidence to reject H0.

b - 2)

From T table,

With test statistics t = -2.18 and df = 99,

p-value = 0.0158

Since p-value < 0.05 level, we have sufficient evidence to reject H0.