Question

The delivery service is a competitive business today with several airports vying to be the highest volume delivery location. Memphis and Louisville are 2 of these airports, home to Fedex and UPS respectively. The number of units (in 1000’s) delivered daily from each of those airports are as follows: Memphis: 485, 534, 650, 554, 550, 572, 487, 533, 526, 410, 515, 578, 497, 592, 448, 469 Louisville: 442, 580, 479, 486, 528, 524, 492, 478, 425, 485, 390, 535. Using alpha = .05, test to determine if there is a significant difference between the 2 airports with respect to the mean number of units delivered daily. Which airport, on average, delivered more packages? Is there any other information that you would like to know? Be specific and explain in a few sentences.

1. State which test you are using
2. State your hypotheses in the correct form (both Ho and Ha).
3. State your rejection rule (in terms of the critical value not in terms of alpha)
4. Calculate your test statistic
5. State your decision made
6. Determine the p-value
7. State your conclusion, in the context of the problem
8. State which type of error you may have made

Answer 1

Here we need to compare mean of two populations so independent sample t test will be used.

Following table shows the output of descriptive statistics:

Descriptive statistics
	Memphis:	Louisville:
count	16	12
mean	525.00	487.00
sample standard deviation	59.4205	51.7476
sample variance	3,530.80	2,677.82
minimum	410	390
maximum	650	580
range	240	190

Since largest standard deviation that is standard deviation of sample 1 is not more than 2 times of smallest standard deviation that is standard deviation of sample 2 so we can assume that population variances are equal.

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Following is the graph:

G:

Conclusion: There are no evidence to conclude that the number of units (in 1000’s) delivered daily from each of those airports are significantly different from each other.

H:

Since we fail to reject the null hypothesis so type II error is possible.