AGR 363 – Homework 6
Due in class on Thursday, 28 March 2019
1. (5 points) Consider the data below which show the time it takes for 20 2017 Chevrolet Camaros to complete (in seconds) the quarter mile. Ten of these Camaros have a 6.2 Liter LT1 V8 engine, while the remaining ten have a supercharged 6.2 Liter LT4 V8 engine.
LT1_V8 3.86 LT4_V8 3.9
LT1_V8 3.79 LT4_V8 3.73
LT1_V8 3.9 LT4_V8 3.61
LT1_V8 3.8 LT4_V8 3.77
LT1_V8 3.83 LT4_V8 3.78
LT1_V8 3.96 LT4_V8 3.72
LT1_V8 4.06 LT4_V8 3.79
LT1_V8 3.87 LT4_V8 3.72
LT1_V8 3.97 LT4_V8 3.82
LT1_V8 3.86 LT4_V8 3.67
LT1_V8 3.84 LT4_V8 3.7
LT1_V8 3.9 LT4_V8 3.72
LT1_V8 3.91 LT4_V8 3.68
LT1_V8 3.83 LT4_V8 3.88
LT1_V8 3.98 LT4_V8 3.72
LT1_V8 3.8 LT4_V8 3.76
LT1_V8 3.89 LT4_V8 3.59
LT1_V8 3.81 LT4_V8 3.78
LT1_V8 3.68 LT4_V8 3.67
LT1_V8 4.09 LT4_V8 3.68
Suppose we are interested in determining whether or not Camaros equipped with an LT4 V8 are faster in the quarter mile than Camaros equipped with an LT1 V8 engine. Assume that the two groups of Camaros are independent.
a. (2 points) Comment on the box plots for the two groups of Camaros (i.e., those equipped with an LT1 V8 engine vs. those equipped with an LT4 V8 engine). Also, perform a hypothesis test of normality. Include the hypotheses, decision, and conclusion. Based on this, make a statement about which of the hypothesis tests we reviewed seems most appropriate for analyzing these data.
b. (3 points) Based on the results from part a.), conduct the most appropriate hypothesis test at
α
= 0.05, and please show all of your work and all seven steps of the hypothesis test. The test of variances is included as well – give the hypotheses, decision, and conclusion for this test. What impact does this have on the test that you need to perform?
2. (5 points) Suppose you decide to take a summer job working at a travel agency, and your boss suspects that Airline A charges more for coach class tickets than Airline B. To assess this suspicion, tickets prices (in US dollars) of flights from O’Hare to 21 randomly selected destinations (same destination for both A and B in each pair) serviced by both airlines were assessed. Below are the ticket prices offered by both Airlines A and B from O’Hare to all 21 destinations.
Destination
|
Airline A
|
Airline B
|
1
|
176.34
|
176.88
|
2
|
296.40
|
220.19
|
3
|
302.76
|
252.77
|
4
|
332.26
|
288.20
|
5
|
396.17
|
291.75
|
6
|
409.74
|
326.25
|
7
|
414.14
|
331.24
|
8
|
419.57
|
336.03
|
9
|
461.52
|
341.58
|
10
|
498.83
|
396.31
|
11
|
525.82
|
422.18
|
12
|
530.91
|
436.86
|
13
|
538.69
|
444.90
|
14
|
542.07
|
491.33
|
15
|
542.71
|
515.41
|
16
|
553.01
|
527.88
|
17
|
587.17
|
543.94
|
18
|
601.07
|
549.27
|
19
|
666.81
|
552.84
|
20
|
709.75
|
622.89
|
21
|
758.93
|
759.91
|
a. (1 points) From the box plots produced of the ticket prices from the two airlines, make a statement about which of the hypothesis tests we reviewed seems most appropriate for analyzing these data.
b. (2 points) Perform a hypothesis test of normality of the distribution of differences. Include the hypotheses, decision, and conclusion. Based on this, make a statement about which of the hypothesis tests we reviewed seems most appropriate for analyzing these data.
c. (2 points) Based on the results from part a.), conduct the most appropriate hypothesis test by hand at
α
= 0.05.
Basic Statistical Measures – difference
|
Location
|
Variability
|
Mean
|
68.38381
|
Std Deviation
|
36.11656
|
Median
|
82.90000
|
Variance
|
1304
|