T Project Essay

1173 words - 5 pages

Introduction
Airline carrier flight times vary slightly from carrier to carrier and even when the airport origins and destinations are the same. Is there a mean difference between San Francisco and Dallas Fort Worth Texas airport in the USA when comparing the flight time between Sky West (OO) and Virgin airlines (VX)? To answer this question, two randomly sampled groups were used to collect data for a two-sample test to conduct a hypothesis which would provide an answer about the mean. I will compare the means of Sky West and Virgin America Airline flight time between San Francisco and Dallas Fort Worth and compare them. I expect the test to reveal the airline with the fastest ...view middle of the document...

Alternative Hypothesis (Ha): There is a significant difference in the population mean in air time of Sky West and Virgin America flights between San Francisco (SFO) and Dallas Fort Worth (DFW) airports in the United States.
Mathematical Terms:
Null hypothesis H₀: µ1 = µ2 vs
Alternative Hypothesis Ha: µ1 ≠ µ2
µ1 = population mean of air time of Virgin America Airline for flights between San Francisco (SFO) and Dallas Fort Worth (DFW) airports in the United States.
µ2 = population mean of air time of Sky West Airline for flights between San Francisco (SFO) and Dallas Fort Worth (DFW) airports in the United States.
The statistical test was a two sample independent study one tailed from the large values in one direction showing significant values, with two tails.
The hypothesis we want to examine in this which is the mean difference in travelling time between both airlines, we specifically want to establish null and an alternative hypothesis that we will be able to evaluate with this data.
The level of significance used in this test is .05 which is the probability of rejecting the null hypothesis when it is true. This is a strong significance although it’s not .001. The test statistic will be a two sample t test since the sample sizes are above n = 50.

Descriptive Statistics
Summary statistics:

Column | n | Mean | Variance | Std. Dev. | Std. Err. | Median | Range | Min | Max | Q1 | Q3 |
VX | 50 | 172.88 | 29.250612 | 5.4083834 | 0.7648609 | 173 | 28 | 156 | 184 | 171 | 176 |
OO | 50 | 172.3 | 40.82653 | 6.389564 | 0.90362084 | 173 | 32 | 158 | 190 | 168 | 175 |

Hypothesis test results:
μ1 : mean of VX
μ2 : mean of OO
μ1 - μ2 : mean difference
H0 : μ1 - μ2 = 0
HA : μ1 - μ2 ≠ 0
Difference | Sample Mean | Std. Err. | DF | T-Stat | P-value |
μ1 - μ2 | 0.58 | 1.1838678 | 98 | 0.48991957 | 0.6253 |

95% confidence interval results:
μ1 : mean of population (Std. Dev. = 5.4083834)
μ2 : mean of population (Std. Dev. = 6.389564)
μ1 - μ2 : mean difference

Difference | n1 | n2 | Sample Mean | Std. Err. | L. Limit | U. Limit |
μ1 - μ2 | 50 | 50 | 0.58 | 1.1838678 | -1.7403382 | 2.9003382 |

Hypothesis test results:
There is no significant difference in the mean travel time for Sky West Airlines (M=172.30, SD=6.39) and Virgin America Airlines (M=172.88, SD=5.41); t (98)= -0.49, p= 0.6253. By looking at these results, you can see the p-value is 0.6253 which is greater than the 0.05 level...

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