Question

Do people walk faster in the airport when they are departing​ (getting on a​ plane) or do they walk faster when they are arriving​ (getting off a​ plane)? A reputable researcher measured the walking speed of random travelers in two International Airports. His findings are summarized in the table. Complete parts ​(a)-(c) below.

Direction of Travel	Departure	Arrival
Mean speed ​(feet per​ minute)	251	269
Standard deviation​(feet per​ minute)	48	34
Sample size	35	35

(a) Is this an observational study or a designed​ experiment? Why?

A.This is an observational study since the researcher did not influence the data.

B.This is a designed experiment since the researcher influenced the data.

C.This is an observational study since the researcher influenced the data.

D.This is a designed experiment since the researcher did not influence the data.

​(b) Explain why it is reasonable to use​ Welch's t-test.

A.The samples are​ random, small and independent.

B.The samples are​ random, large and independent.

C.The populations are normally distributed.

D.The samples are​ random, large and dependent.

​(c) Do individuals walk at different speeds depending on whether they are departing or arriving at the α=0.05 level of​ significance? Let μ1 represent the mean speed of people departing and μ2 represent the mean speed of people arriving.

State the null and alternative hypothesis.

A. H0​: μ1=μ2

H1​:=μ1<μ2

B. H0​: μ1<μ2

H1​:μ1>μ2

C. H0​:μ1=μ2

H1​:μ1≠μ2

D. H0​: μ1=μ2

H1​:μ1>μ2

Determine the​ P-value for this hypothesis test.

​P-value =_____ ​(Round to three decimal places as​ needed.)

Choose the correct conclusion.

A. Do not reject H0. There is not sufficient evidence at the α=0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.

B.Reject H0. There is not sufficient evidence at the α=0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.

C.Do not reject H0. There is sufficient evidence at the α=0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.

D. Reject H0. There is sufficient evidence at the α=0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.

Answer 1

a) A.This is an observational study since the researcher did not influence the data.

b)

C. H0​:μ1=μ2

H1​:μ1≠μ2

c)

A. Do not reject H0. There is not sufficient evidence at the α=0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.