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# To decrease the amount of time it takes to deliver packages,

### Resolved Question:

To decrease the amount of time it takes to deliver packages, a delivery company purchased computer software that finds the optimal route for making deliveries based upon the input of the package destinations. In the past the average amount of time it took to complete deliveries was 9.4 hours with a standard deviation of 0.8 hours. Since purchasing the software the average delivery time over twenty delivery days was 8.6 hours. At the 0.05 level of significance, test whether the software package has reduced the average time it takes to complete deliveries.
Submitted: 5 years ago.
Category: Math Homework
Expert:  Scott replied 5 years ago.

Hi there,

H0: μ > 9.4

Ha: μ < 9.4

The critical value for the 0.05 significance level, with one tail is:

z = -1.645

(from a z table)
We'll reject H0 if our test statistic is below that.

Test stat:

z = (x-mu)/(s/sqrt(N))

z = (8.6-9.4)/(0.8/sqrt(20))

z = -4.472

That is below the critical value.

Therefore, we reject H0.

That means that the software package has reduced the time.

Let me know if you have any questions,

Scott