Answer:
(a) <em>H₀</em>: <em>μ</em> = 10 vs. <em>Hₐ</em>: <em>μ</em> < 10.
(b) The level of significance is 0.05.
Step-by-step explanation:
A new system is used to reduce the time customers spend waiting for teller service during peak hours at a bank.
A single mean test can be used to determine whether the waiting time has reduced.
(a)
The hypothesis to test whether the new system is effective or not is:
<em>H₀</em>: The mean waiting time is 10 minutes, i.e. <em>μ</em> = 10.
<em>Hₐ</em>: The mean waiting time is less than 10 minutes, i.e. <em>μ</em> < 10.
(b)
The information provided is:
Compute the test statistic value as follows:
The test statistic value is <em>t</em> = -1.902.
Compute the <em>p</em>-value of the test as follows:
The null hypothesis will be rejected if the <em>p</em>-value of the test is less than the significance level (<em>α</em>).
The <em>p</em>-value obtained is 0.031.
To reject the null hypothesis the value of <em>α</em> should be more than 0.031.
The most commonly used values of <em>α</em> are: 0.01, 0.05 and 0.10.
So, the least value of <em>α</em> at which we can conclude that the wait times have decreased is, <em>α</em> = 0.05.
Thus, the level of significance is 0.05.