For problems 1 through 3, state the claim and its opposite and the null and alte
ID: 3221535 • Letter: F
Question
For problems 1 through 3, state the claim and its opposite and the null and alternate hypotheses, the type of analysis that should be performed (either testing inferences about two proportions, means from independent samples, or means from matched pairs), and the formula used to calculate the test statistic. Show the values substituted into the formula, and calculate the value of the test statistic, draw and label a graph, determine the P-value, state what to do with the null hypothesis, and use the flow chart to state your conclusion. Assume that the samples are simple random samples and all requirements are satisfied.
1. Researcher Seth B. Young measured the walking speed of business and leisure travelers in San Francisco International Airport and Cleveland Hopkins International Airport. His findings are summarized below. Test the claim that business travelers walk faster than leisure travelers at 0.05 level of significance.
Traveler
Mean speed (ft per min)
St Dev (ft per min)
Sample size
Business
272
43
20
Leisure
261
47
20
Traveler
Mean speed (ft per min)
St Dev (ft per min)
Sample size
Business
272
43
20
Leisure
261
47
20
Explanation / Answer
We can formulate the hypothesis as
at 0.05 level of significance.
H0 : The business travelers do not walk faster than leisure travelers
H1 : The business travelers walk faster than leisure travelers
The test can be formulated as
Traveler
Mean speed (ft per min)
St Dev (ft per min)
Sample size
Business
272
43
20
Leisure
261
47
20
Test statistic. The test statistic is a t statistic (t) defined by the following equation.
t = [ (x1 - x2) - d ] / SE
and SE = sqrt[ (s12/n1) + (s22/n2) ]
here n1=n2 = 20 and
SE = sqrt[ (432/20) + (472/20) ] = 14.24
here
t = [ (272 - 261) ] / 14.24 = 0.7724
now the df would be
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
(((43^2)/20 + (47^2)/20)^2) / (((((43^2)/20)^2)/(19)) + ((((47^2)/20)^2)/(19))) = 37.7 = 38
so the critical value for the df is
for the 1 tail t test the critical value is 1.685
as the tstat < tcritcal , hence we fail to reject the null hypothesis and conclude that The business travelers do not walk faster than leisure travelers
Hope this helps !! Please rate !!
Traveler
Mean speed (ft per min)
St Dev (ft per min)
Sample size
Business
272
43
20
Leisure
261
47
20
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