Respuesta :
Answer:
(a) H₀: μ = 10 vs. Hₐ: μ < 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:
H₀: The mean waiting time is 10 minutes, i.e. μ = 10.
Hₐ: The mean waiting time is less than 10 minutes, i.e. μ < 10.
(b)
The information provided is:
[tex]\bar x=9.5\\s=2.2\\n=70[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{9.5-10}{2.2/\sqrt{70}}=-1.902[/tex]
The test statistic value is t = -1.902.
Compute the p-value of the test as follows:
[tex]p-value=P(t_{n-1}<t)[/tex]
[tex]=P(t_{69}<-1.902)\\=P(t_{69}>1.902)\\=0.031[/tex]
The null hypothesis will be rejected if the p-value of the test is less than the significance level (α).
The p-value obtained is 0.031.
To reject the null hypothesis the value of α should be more than 0.031.
The most commonly used values of α are: 0.01, 0.05 and 0.10.
So, the least value of α at which we can conclude that the wait times have decreased is, α = 0.05.
Thus, the level of significance is 0.05.
