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)	256	269
Standard deviation​(feet per​ minute)	53	37
Sample size	35	35

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

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

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

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

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

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

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

B. The populations are normally distributed.

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

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 a=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. Upper H 0H0​:

mu 1 less than mu 2μ1<μ2

Upper H 1H1​:

mu 1 greater than mu 2μ1>μ2

B. Upper H 0H0​:

mu 1 equals mu 2μ1=μ2

Upper H 1H1​:

mu 1 greater than mu 2μ1>μ2

C. Upper H 0H0​:

mu 1 equals mu 2μ1=μ2

Upper H 1H1​:

mu 1 less than mu 2μ1<μ2

D. Upper H 0H0​:

mu 1 equals mu 2μ1=μ2

Upper H 1H1​:

mu 1 not equals mu 2

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 not reject H0. There is

sufficient evidence at the a=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 a=0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.

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

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

Answer 1

(a) The correct option is (B) , i.e.This is an observational study since the researcher did not influence the data.

Since the researchers only collected the sample and studied the sample, so this does not make any influence on the data, that's why it is a observational study

(b) The correct option is (A) The samples are​ random, large and independent.

The condition of normality for population is must, but since the sample sizes are so that suffices the normality condition for Welch's t-test.

(c) The correct option is (D), i.e.,

Welch's t-test statistic:

Now the walking speed of random travellers in two International Airports for their Departure and Arrival is given in the question -

For Departure:

For Arrival:

So, the test-statistic is calculated as

Degrees of freedom(df):

p-value:

test-statistic, and df=60

Conclusion:

The correct option is (D) Do not reject H0.There is not sufficient evidence at the a=0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.

Since,

So, at there is not sufficient evidence to support the alternative hypothesis, i.e., . Hence we conclude that the mean speed(foot per minute) for travellers at arriving and departing the airport is not different .