The bank manager wants to show that the new system reduces typical customer wait

Question

The bank manager wants to show that the new system reduces typical customer waiting times to less than 6 minutes. One way to do this is to demonstrate that the mean of the population of all customer waiting times is less than 6. Letting this mean be µ, in this exercise we wish to investigate whether the sample of 94 waiting times provides evidence to support the claim that µ is less than 6.

Find the mean and standard deviation of the population of all possible sample means when we assume that µ equals 6. (Round your answer to 4 decimal places.)

If µ equals 6, what percentage of all possible sample means are less than or equal to 5.60? What do you conclude about whether the new system has reduced the typical customer waiting time to less than 6 minutes? (Round your answer to 2 decimal places.)

The bank manager wants to show that the new system reduces typical customer waiting times to less than 6 minutes. One way to do this is to demonstrate that the mean of the population of all customer waiting times is less than 6. Letting this mean be µ, in this exercise we wish to investigate whether the sample of 94 waiting times provides evidence to support the claim that µ is less than 6.

      For the sake of argument, we will begin by assuming that µ equals 6, and we will then attempt to use the sample to contradict this assumption in favor of the conclusion that µ is less than 6. Recall that the mean of the sample of 94 waiting times is = 5.60 and assume that , the standard deviation of the population of all customer waiting times, is known to be 2.20.

Explanation / Answer

a) shape of this population of sample means will be approximately normal.

Normal because the sample is large

b)mean =6

std deviation =2.2/(94)1/2 =0.2269

c)P(X<5.6)=P(Z<(6-5.6)/0.2269)=P(Z<-1.7628)=0.0390

d)

3.9 % ; conclude that µ is less than 6. as p is less then 0.05.

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