Question

A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-1:00pm lunch period. The waiting time of all customers during this hour is recorded over the period of a week. A random sample of 30 customers is selected and their waiting time is recorded (see data file Bank 1). At the 0.05 level of significance is there evidence that the population mean waiting time is less than 5 minutes?

4.21 |

5.55 |

3.02 |

5.13 |

4.77 |

2.34 |

3.54 |

3.20 |

4.50 |

6.10 |

0.38 |

5.12 |

6.46 |

6.19 |

3.79 |

4.21 |

5.55 |

3.02 |

5.13 |

4.77 |

2.34 |

3.54 |

3.20 |

4.50 |

6.10 |

0.38 |

5.12 |

6.46 |

6.19 |

3.79 |

Usethe full 5 step hypothesis testing procedure as demonstrated in class.

**Identify information given in the question**.

1**. Select appropriate test statistic**

**2. State Hypotheses: (Null and
Alternative)**

**3. Determine critical value(s) and state
decision rules.**

**4. Collect data and compute test
statistic**

**5. a. Make a Decision
:**

**- either reject the
null**

**- or fail to reject (FTR) the
null.**

**b. State the managerial conclusion**

Answer #1

Step 1: Stating the null and alternative hypothesis

Let denote the population mean waiting time.

To test: Vs

Step 2: Test statistic and Significance level

Test statistic appropriate here, is given by

(We chose t test for testing the mean since, the population variance is unknown)

From the given data,

Given that n = 30 and significance level is fixed at 0.05.

Step 3. Decision rule

Since our test is left tailed, the decision rule, here, is to
reject H_{0} when

From t tables,

Hence, the rejection region is

Step 4. Compute the test statistic:

From the given data,

And given that n = 30, substituting the values obtained in the test statistic formula:

Since, t = -2.428 < -1.699, the test statistic falls in the rejection region.

Step 5. Interpretation

Since, the test statistic falls in the rejection region, we may
reject H_{0} at 5% level of significance. It implies that
we have sufficient evidence to support our claim that the
population mean waiting time is less than 5 minutes based on the
given data.

Hence we may conclude that population mean waiting time of the customers is less than 5 minutes.

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business objective of developing an improved process for serving
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line to when he or she reaches the teller window. Data collected
from a sample of 15 customers during this hour are stored as
follows:
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Please show me how to use R to solve the problem. thanks!
A bank with a branch located in a commercial district of a city
has developed an improved process for serving customers during the
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reducing the waiting time (defined as the number of minutes that
elapse from when the customer enters the line until he or she
reaches the teller window) to increase customer satisfaction. A
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A bank branch located in a commercial district of a city has the
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during the noon-to-1:00 P.M. lunch period. The waiting time is
defined as the time the customer enters the line until he or she
reaches the teller window. The bank wants to determine if the mean
waiting time is less than 5 minutes. A random sample of 15
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A bank branch located in a commercial district of a city has the
business objective of improving the process for serving customers
during the noon-to-1:00 P.M. lunch period. The waiting time
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