In: Statistics and Probability
4. Do people walk faster in airport when they are departing or when they are arriving? A researcher measured the walking speed of travelers in an airport and his finding is shown below:
Departure |
Arrival |
|
Mean speed (feet per minute) |
265 |
274 |
Standard deviation(feet per minute) |
52 |
35 |
Sample size |
40 |
40 |
Do individuals walk at different speeds depending on whether they are departing or arriving at the α=0.05 level of significance?
Given
n | Mean (M) | Standard Deviation (SD) | |
Departure | n1 = 40 | M1 = 265 | s1 = 52 |
Arrival | n2 = 40 | M2 = 274 | s2 = 35 |
The null and alternative hypotheses are
Ho : μ1 = μ2
Ha : μ1 ≠ μ2
where μ1 = μ2 are population mean speeds of people
during Departure and Arrival respectively
α =
0.05
...Level of significance
We use independent Samples T test since population standard
deviation is unknown
Using the given formulae, we get
Degrees of Freedom
df1 = n1 - 1 , df2 = n2 - 1 , df = n1 + n2 - 2 = 40 + 40 - 2 =
78
df = 78
Pooled Variance
Sp2 = 1964.5
Mean Squared Error Sm1-m2
Sm1-m2 = 9.9109
t-statistic
t-statistic = t = -0.9081
P-value
For t = -0.9081, df = 78 we find the two tailed p-value using t
tables or Excel function t.dist.2t
p-value = t.dist.2t(abs(-0.9081), 78)
p-value = 0.3666
Decision
0.3666 > 0.05
that is p-value is greater than alpha.
Hence we DO NOT Reject Ho.
Conclusion
There does not exist enough statistical evidence at α = 0.05 to
show that individuals walk at different speeds depending on whether
they are departing or arriving.
that is,
Individuals do not walk at different speeds depending on whether they are departing or arriving.
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