Answer:
Both the approach gave the same conclusion:
There is enough evidence to support the claim that the mean waiting time is shorter than six minutes
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 6 minutes
Sample mean, = 5.46 minutes
Sample size, n = 100
Alpha, α = 0.05
Sample standard deviation, s = 2.475 minutes
First, we design the null and the alternate hypothesis
We use one-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
a) Use the critical value approach
Now, Since, the calculated test statistic is less than the critical value of t, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Conclusion:
Thus, there is enough evidence to support the claim that new system reduces the time customers spend waiting for teller service during peak hours from the current 9 to 10 minutes to less than 6 minutes.
b) Use the p-value approach
The p-value can be calculated as:
P-value = 0.0055
Since the p-value is less than the significance level, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Conclusion:
Thus, there is enough evidence to support the claim that new system reduces the time customers spend waiting for teller service during peak hours from the current 9 to 10 minutes to less than 6 minutes.