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ArbitrLikvidat [17]
3 years ago
5

A bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The m

anager hopes the new system will reduce the waiting time that currently is 10 minutes. (a) Formulate the null and alternative hypotheses for this problem. (b) A random sample of 70 waiting times was obtained after the system was implemented. The sample showed a sample mean of 9.5 minutes and a standard deviation of 2.2 minutes. At what level of significance can you conclude that wait times have decreased?
Mathematics
1 answer:
Lana71 [14]3 years ago
6 0

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:

\bar x=9.5\\s=2.2\\n=70

Compute the test statistic value as follows:

t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{9.5-10}{2.2/\sqrt{70}}=-1.902

The test statistic value is <em>t</em> = -1.902.

Compute the <em>p</em>-value of the test as follows:

p-value=P(t_{n-1}

               =P(t_{69}1.902)\\=0.031

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.

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