Question

In: Statistics and Probability

Do people walk faster in the airport when they are departing​ (getting on a​ plane) or...

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 influenced the data. B. This is an observational study since the researcher influenced 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 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 samples are​ random, large and dependent. D. The populations are normally distributed. ​(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 not equals 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 greater than mu 2 D. Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 less than mu 2 Determine the​ P-value for this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) Choose the correct conclusion. A. 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. B. 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. C. 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 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. Click to select your answer(s).

Direction of Travel

Departure

Arrival

Mean speed

​(feet per​ minute)

258258

274274

Standard deviation​(feet per​ minute)

4747

3030

Sample size

3535

35

Solutions

Expert Solution

(a)

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

Explanation: In an observational study,there is no influence with any of the variables being studied and the results are simply recorded based on the observation. As against in an experiment, the variables are treated with treatments and the results are then recorded and studied.

(b)

D. The populations are normally distributed.

Explanation: Welch's test is used to test 2 samples having unequal variances. Like every other hypothesis testing the samples are independent and random but most importantly for Welch's t-test ,the samples come from normal population.

(c)

A. Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 not equals mu 2

Explanation: Initially it is assumed that there is no difference between the walking of people departing or arriving. Hence,the null hypothesis. But the question asks whether there is a difference or not between the speed. It does not specifically ask whether one is faster or slower than the other. Hence,the alternative hypothesis.

(d)

D. 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.

All the given information

There seems to be a mistake in the values since the degrees of freedom round approximate to 0. But I according to my understanding I think following are correct values. Apologies if I am incorrect.

According to the question

Test Statistic=

Substituting the values

Degrees of freedom = where

Substituting

= 57.76 approx 58

Since this a 2 tailed t-test

Critical value

Decision Criteria: Reject null hypo if T.S. > Critical value

1.6976 < 2.3010

Decision: We do not reject the null hypothesis at 5% level of significance and conclude that there is no significant difference between the walking speed of people while departing and arriving.


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