The British Department of Transportation studied to see if people avoid driving
ID: 3370126 • Letter: T
Question
The British Department of Transportation studied to see if people avoid driving on Friday the 13th. They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations ("Friday the 13th," 2013). The data for each location on the two different dates is in following table:
Table: Traffic Count
Dates
6th
13th
1990, July
139246
138548
1990, July
134012
132908
1991, September
137055
136018
1991, September
133732
131843
1991, December
123552
121641
1991, December
121139
118723
1992, March
128293
125532
1992, March
124631
120249
1992, November
124609
122770
1992, November
117584
117263
Let ?1= mean traffic count on Friday the 6th. Let ?2 = mean traffic count on Friday the 13th. Estimate the mean difference in traffic count between the 6th and the 13th using a 90% level.
(i) Determine the sample mean of differences x??di Determine the sample mean of differences x¯d
Enter in decimal form to nearest tenth.
(ii) Determine sample standard deviation of differences sd
Enter in decimal form to nearest hundredth. Examples of correctly entered answers:
0.01 0.20 0.35 3.00
(iii) Enter the level of significance ? used for this test:
Enter in decimal form. Examples of correctly entered answers: 0.01 0.02 0.05 0.10
(iv) Determine degrees of freedom for the sample of differences dfd:
Enter value in integer form. Examples of correctly entered answers:
2 5 9 23 77
(v) Determine t - score associated with critical value: tc
Enter in decimal form to nearest thousandth. Examples of correctly entered answers:
0.0011 0.020 0.500 0.371 2.000
(vi) Determine "error bound of the mean of difference" E
Enter value in decimal form rounded to nearest tenth. Examples of correctly entered answers:
2.0 0.3 1.6 11.7
(vii) Determine confidence interval of the mean difference ?d
Enter lower bound value to nearest tenth, followed by < , followed by "?d" for mean difference, followed by <, followed by upper bound value to nearest tenth. No spaces between any characters. Use "negative" sign if necessary. Do not use italics or enter units of measure. Examples of correctly entered answers:
0.74<?d<0.78
13.14<?d<13.96
-9.72<?d<-8.08
(viii) Using the confidence interval, select the correct description of the result of the survey:
A. We estimate with 90% confidence that the true population mean traffic count between Friday the 6th and Friday the 13th is between 1154.1 and 2517.5.
B. We estimate with 90% confidence that the true mean difference in traffic counts between Friday the 6th and Friday the 13th falls outside 1154.1 and 2517.5.
C. We estimate with 90% confidence that the true sample mean traffic counts between Friday the 6th and Friday the 13th is between 1154.1 and 2517.5.
D. We estimate with 90% confidence that the true mean difference in traffic counts between Friday the 6th and Friday the 13th is between 1154.1 and 2517.5.
Enter letter corresponding to most correct answer
Dates
6th
13th
1990, July
139246
138548
1990, July
134012
132908
1991, September
137055
136018
1991, September
133732
131843
1991, December
123552
121641
1991, December
121139
118723
1992, March
128293
125532
1992, March
124631
120249
1992, November
124609
122770
1992, November
117584
117263
Explanation / Answer
(i) since, mean(6th)=128385.3 and mean(13th)= 126549.5 then sample mean of differences,
Answer: (mean(6th)-mean(13th))=1835.8
(ii) sample standard deviation of difference=sqrt(s1^2+s2^2 )
=10556.40
(iii) level of significance=0.10
(iv) degree of freedom=(10+10-2)=18
(v) critical value of t = see the t-table at 18 d.f. at 0.10 of two tailed test=1.734 .
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