1. A local indian restaurant advertises home delivery times of 30 minutes. To mo

Question

1. A local indian restaurant advertises home delivery times of 30 minutes. To monitor effectiveness of this promise the restaurant manager monitors the time that the order was received and the time of delivery. Based upon historical data the average time for delivery is 30 minutes with a standard deviation of 5 minutes. After a series of complaints from customers regarding this promise the manager decided to analyze the last 50 orders which resulted in an average of 32 minutes. Conduct an appropriate test at a significance level of 5%. should the manager be concerned.

Explanation / Answer

Set Up Hypothesis
Null Hypothesis H0: U=30
Alternate Hypothesis H1: U!=30
Test Statistic
Population Mean(U)=30
Given That X(Mean)=32
Standard Deviation(S.D)=5
Number (n)=50
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=32-30/(5/Sqrt(50)
Zo =2.8284
| Zo | =2.8284
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.8284 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != 2.8284 ) = 0.0047
Hence Value of P0.05 > 0.0047, Here we Reject Ho

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