A Chicago-based firm has documents that must be quickly distributed to district offices throughout the U.S. The firm must de- cide between two delivery services, UPX (United Parcel Express) and INTEX (International Express), to transport its documents. In testing the delivery times of the two services, the firm sent two reports to a random sample of its district offices with one report carried by UPX and the other report carried by INTEX. Do the data on the next slide indicate a difference in mean delivery times for the two services? Use a .05 level of significance. [Hint: Perform a hypothesis test for difference for matched/paired samples, D = X1 − X2]   (d) Find the critical values. (e) Rejection region and conclusion. (f) Interpret the results.

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A Chicago-based firm has documents that must be quickly distributed to district offices throughout the U.S. The firm must de- cide between two delivery services, UPX (United Parcel Express) and INTEX (International Express), to transport its documents. In testing the delivery times of the two services, the firm sent two reports to a random sample of its district offices with one report carried by UPX and the other report carried by INTEX. Do the data on the next slide indicate a difference in mean delivery times for the two services? Use a .05 level of significance. [Hint: Perform a hypothesis test for difference for matched/paired samples, D = X1 − X2]

 

(d) Find the critical values.

(e) Rejection region and conclusion.

(f) Interpret the results.

### Distribution of UPX and INTEX by District Office

This table provides quantitative data on the distribution of two variables, UPX (X₁) and INTEX (X₂), across various district offices. 

| District Office | UPX (X₁) | INTEX (X₂) |
|-----------------|----------|------------|
| Seattle         | 32       | 25         |
| Los Angeles     | 30       | 24         |
| Boston          | 19       | 15         |
| Cleveland       | 16       | 15         |
| New York        | 15       | 13         |
| Houston         | 18       | 15         |
| Atlanta         | 14       | 15         |
| St. Louis       | 10       | 8          |
| Milwaukee       | 7        | 9          |
| Denver          | 16       | 11         |

#### Analysis

- **Seattle and Los Angeles** have the highest values for both UPX and INTEX, indicating strong activity in these regions.
- **Milwaukee and St. Louis** report the lowest numbers, potentially highlighting lower engagement or output.
- **Boston, Cleveland, Houston, and Atlanta** show similar INTEX numbers (15), although their UPX values vary.

This data might be utilized for analyzing regional performance, resource allocation, or strategic planning.
Transcribed Image Text:### Distribution of UPX and INTEX by District Office This table provides quantitative data on the distribution of two variables, UPX (X₁) and INTEX (X₂), across various district offices. | District Office | UPX (X₁) | INTEX (X₂) | |-----------------|----------|------------| | Seattle | 32 | 25 | | Los Angeles | 30 | 24 | | Boston | 19 | 15 | | Cleveland | 16 | 15 | | New York | 15 | 13 | | Houston | 18 | 15 | | Atlanta | 14 | 15 | | St. Louis | 10 | 8 | | Milwaukee | 7 | 9 | | Denver | 16 | 11 | #### Analysis - **Seattle and Los Angeles** have the highest values for both UPX and INTEX, indicating strong activity in these regions. - **Milwaukee and St. Louis** report the lowest numbers, potentially highlighting lower engagement or output. - **Boston, Cleveland, Houston, and Atlanta** show similar INTEX numbers (15), although their UPX values vary. This data might be utilized for analyzing regional performance, resource allocation, or strategic planning.
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