Question

Direction of Travel Departure Arrival Mean speed ​(feet per​ minute) 257 268 Standard deviation​ (feet per​ minute) 52 38 Sample size 35 35 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. LOADING... Click the icon to view the findings. ​(a) Is this an observational study or a designed​ experiment? Why? A. This is a designed experiment 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 an observational study 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 populations are normally distributed. C. The samples are​ random, large 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 alphaequals0.05 level of​ significance? Let mu 1 represent the mean speed of people departing and mu 2 represent the mean speed of people arriving. State the null and alternative hypothesis. A. Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 less than mu 2 B. Upper H 0​: mu 1 less than mu 2 Upper H 1​: mu 1 greater than mu 2 C. Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 not equal mu 2 D. Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 greater than mu 2 Determine the​ P-value for this hypothesis test. ​P-value equals nothing ​(Round to three decimal places as​ needed.) Choose the correct conclusion. A. Reject Upper H 0. There is sufficient evidence at the alphaequals0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing. B. Reject Upper H 0. There is not sufficient evidence at the alphaequals0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing. C. Do not reject Upper H 0. There is not sufficient evidence at the alphaequals0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing. D. Do not reject Upper H 0. There is sufficient evidence at the alphaequals0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.

DATA:

Direction of Travel	Departure	Arrival
Mean speed ​(feet per​ minute)	257	268
Standard deviation​(feet per​ minute)	52	38
Sample size	35	35

Answer 1

Answer to (a):-
D. This is an observational study since the researcher did not influence the data.

Explanation:-
This is an observational study since the researcher did not influence the data. The researcher observed random travelers shows that the data he collected was irrespective of any external interventions.

Answer to (b):-
C. The samples are​ random, large and independent.
Explanation:-
It is reasonable to use the Welch's t test because the samples are random, large and independent.
In statistics, a sample size(n)>30 is treated as a large sample, as in this case. Since the people were chosen at random, their actions were all independent of each others'.Hence the sample was independent.

Answer to (c):-
C. Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 not equal mu 2
Explanation:-
The option c. would be correct which says Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 not equal mu 2. It depicts that the test will be a two-tailed test. It woukd have been a right tailed ot left tailed test if the question mentioned to check if the departure speed
is is more or less than the arrival speed, or otherwise. This hypotheses would only check if the two speeds differ or not.

Answer to (d). :-
C. Do not reject Upper H 0. There is not sufficient evidence at the alphaequals0.05 level of significance to say that travelers walk at different speeds depending on whether they are arriving or departing.

Explanation:
The t stat, on calculation was found out to be 1.011, which lies in the acceptance region of the graph because it is less than the critical value(df=33 and sig.=0.05).
So we do not have enough evidence to reject the null hypothesis and say that travelers walk at different speeds depending on whether they are arriving or departing.