Do individuals walk at different speeds depending on whether they are departing or arriving at the α = 0.01 level of significance? Let μ1 represent the mean speed of people departing and μ2 represent the mean speed of people arriving.
(a) State the null and alternative hypothesis.
(b) Determine the P-value for this hypothesis test. Round to three decimal places as needed.
Data Summary
n | Mean (M) | Variance (SS) | Standard Deviation (SD) | |
Departure | n1 = 35 | M1 = 251 | SS1 = 2116 | s1 = 46 |
Arrival | n2 = 35 | M2 = 270 | SS2 = 1521 | s2 = 39 |
a)
The null and alternative hypotheses are
Ho : μ1 =
μ2
Ha : μ1 ≠ μ2
where μ1 , μ2 are the
population mean walking speeds of people departing and arriving
respectively
α =
0.01
... 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 = 35 + 35 - 2 =
68
df = 68
Pooled
Variance
Sp2 = 1818.5
Mean Squared Error
Sm1-m2
Sm1-m2 = 10.1938
t-statistic
t-statistic = t = -1.8639
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b)
P-value
For t = -1.8639, df = 68 we find the two tailed p-value using t
tables or Excel function t.dist.2t
p-value = t.dist.2t(abs(-1.8639), 68)
p-value = 0.067
Decision
0.067 > 0.01
that is p-value is greater than alpha.
Hence we DO NOT Reject Ho.
Conclusion
There does not exist enough statistical evidence at α = 0.01 to
show that people walk at different speeds while departing or
arriving.
that is, the walking speeds are not different while departing or arriving
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