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You are considering a new delivery system and wish to test whether the new system will...

You are considering a new delivery system and wish to test whether the new system will conform to your requirements at a 5% significance level. It is well established that the mean delivery time of the current system is 2.38 days. The specifications of the new delivery system state that the average variation (standard deviation) of the delivery times is 0.43 days. To test the new system, we have data for 48 delivery times. For the sample, the average delivery time of the new system is 2.23 days.

You would like to test if the average delivery time of the new system is significantly different from that of the old system

What is the test statistic?

What is the critical value?

What is the rejection region?

What is the p-value?

I would really appreciate some solving these with an in depth explanation of the formulas needed.

math   Statistics-And-Probability   
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Answer #1

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (2.23 - 2.38)/(0.43/sqrt(48))
z = -2.42


Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96


P-value Approach
P-value = 0.0155
As P-value < 0.05, reject the null hypothesis.

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