Question

The management for a large grocery store chain would like to
determine if a new cash register will enable cashiers to process a
larger number of items on average than the cash register which they
are currently using. Nine cashiers are randomly selected, and the
number of grocery items which they can process in three minutes is
measured for both the old cash register and the new cash
register.

Without making any assumptions about the distribution, do the data
provide conclusive evidence that the new cash register enables
cashiers to process a significantly larger number of items than the
old cash register? Use the Wilcoxon signed-rank test to analyze the
results.

Cashier | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 |
---|---|---|---|---|---|---|---|---|---|

Old Cash Register | 6464 | 6666 | 5858 | 6666 | 6262 | 5757 | 6060 | 6767 | 7878 |

New Cash Register | 6363 | 7373 | 6464 | 6868 | 5858 | 6565 | 6262 | 7777 | 7373 |

Step 1 of 2:

Find the value of the test statistic to test if the new cash register enables cashiers to process a significantly larger number of items than the old cash register. Round your answer to two decimal places, if necessary.

Step 2 of 2:

Make the decision to reject or fail to reject the null hypothesis that the number of items that the new cash register enables cashiers to process is less than or equal to the number of items that the old cash register enables cashiers to process, and state the conclusion in terms of the original problem. Use α=0.01α=0.01.

Answer #1

Step 1 of 2:

-1.48

Step 2 of 2:

The p-value from the output is 0.0693.

Since the p-value (0.0693) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Therefore, we cannot support the claim that the new cash register enables cashiers to process a significantly larger number of items than the old cash register.

variables: | Old Cash Register - New Cash Register | |

10 | sum of positive ranks | |

35 | sum of negative ranks | |

9 | n | |

22.500 | expected value | |

8.441 | standard deviation | |

-1.48 | z | |

.0693 | p-value (one-tailed, lower) | |

No. | Data | Rank |

1 | 101 | 1 |

2 | -707 | 7 |

3 | -606 | 6 |

4 | -202 | 2.5 |

5 | 404 | 4 |

6 | -808 | 8 |

7 | -202 | 2.5 |

8 | -1010 | 9 |

9 | 505 | 5 |

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