Question

Please show your work

9.2.6

The British Department of Transportation studied to see if people avoid driving on Friday the 13^th.   They did a traffic count on a Friday and then again on a Friday the 13^th at the same two locations ("Friday the 13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean difference in traffic count between the 6^th and the 13^th using a 90% level.

Table #9.2.6: 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

Answer 1

Sol:

Using SPSS,

The difference in the mean may be estimated and tested at 90% level using a paired t test, since the observations on the 2 days are depenedent ( Since obtained from the same location ).

Conducting a paired t teast using these data yields the following results:

The mean difference estimated at 90% level has the value

The sample mean of difference is the mean of the difference in the paired value in each sample observation = 1835.8

The sample standard deviation of differences sd = 1176.01

Level of significance ? used for this test = 0.10

Degrees of freedom for the sample of differences (dfd) = No. of paired observations - 1

= 10 - 1 = 9

t - score associated with critical value (tc)

= t = Sample mean of difference / [Its standard deviation / sqrt ( No. of paired observations)]

t = 4.936

The estimated mean difference Error bound = Confidence interval for actual mean difference

Substituting the lower and upper bounds, we obtain the error bound as 681.7

Confidence interval of the mean difference ?d :

1154.1 < < 2517.5

The correct description would be

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.