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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 packages destinations.  In the past the average amount of time it took to come delivery 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 delivery.
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1 Answer

"Average" implies you will use the mean (μ):
 
μ = 9.4 hrs.   n =20 days (since σ is known use z-test) 
σ = 0.8 hrs.   x-bar(sample mean) =8.6 hrs.
 
level of significance==>α = 0.05 (one-tail test since claim < )
 
H0 : μ ≥ 9.4
H1 : μ < 9.4 (Claim)
 
Using Graphing Calculator TI-83/TI-83Plus:
Go to STATS, TESTS, 1:Z-Test, Stats, μ0:9.4, σ: 0.8, x-bar: 8.6, n:20, μ: < μ0, Calculate
 
Test statistic:  z= -4.47
p-value: 3.876E-6 = .000003876
 
Since p-value(.000003876)<level of significance(α=.05), then reject null hypothesis(H0) and support claim that software did reduce average delivery time.
 
 
 

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