Question

In: Statistics and Probability

4. Do people walk faster in airport when they are departing or when they are arriving?...

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?

Solutions

Expert Solution

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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