PFA

A data set can be found at the Data and Story Library site: http://lib.stat.cmu.edu/DASL)by searching for Friday the 13th materials.

The data were collected in an effort to study various aspects of human behavior on Friday 13th by monitoring the change in traffic patterns between Friday the 6th and the subsequent Friday the 13th along with shopping traffic and accident reports.
A. Use the data in the accident category from the Friday the 13th data file, along with an appropriate hypothesis test to answer the question: Is Friday the 13th any more unlucky than Friday the 6th?

accident 1989, October 9 13 SWTRHA hospital
accident 1990, July 6 12 SWTRHA hospital
accident 1991, September 11 14 SWTRHA hospital
accident 1991, December 11 10 SWTRHA hospital
accident 1992, March 3 4 SWTRHA hospital
accident 1992, November 5 12 SWTRHA hospital

To see if there is a difference in the number of accidents, we're going to use a two-sample t-test to compare the mean number of accidents on the 6th of the month and the 13th of the month.

The alternative hypothesis is that there are more accidents on the 13th than on the 6th, and the null hypothesis is that the number of accidents on the 13th is less than or equal to the number on the 6th. We will be using a one-sided test.
The test statistic is calculated as

(let x represent data from the 6th and y represent data from the 13th). There are 10 degrees of freedom (df = n1 + n2 - 2).

If you calculate the mean and standard deviations of the data (you should get mean = 7.5, sd = 3.33 for the 6th and mean = 10.8 and sd = 3.6 for the 13th) and calculate the test statistic, you will get t = -1.66. If you compare this to a t-distribution with 10 degrees of freedom, you will find that the means of the two groups are NOT significant (p = 0.064). Therefore, there is NOT evidence that Fridays the 13th are unlucky.

B. Do more people shop on Friday the 13th? Justify your answer by formulating and executing a hypothesis test.
shopping 1990, July 4942 4882 Epsom
shopping 1991, September 4895 4736 Epsom
shopping 1991, December 4805 4784 Epsom
shopping 1992, March 4570 4603 Epsom
shopping 1992, November 4506 4629 Epsom
shopping 1990, July 6754 6998 Guildford
shopping 1991, September 6704 6707 Guildford
shopping 1991, December 5871 5662 Guildford
shopping 1992, March 6026 6162 Guildford
shopping 1992, November 5676 5665 Guildford
shopping 1990, July 3685 3848 Dorking
shopping 1991, September 3799 3680 Dorking
shopping 1991, December 3563 3554 Dorking
shopping 1992, March 3673 3676 Dorking
shopping 1992, November 3558 3613 Dorking
shopping 1990, July 5751 5993 Chichester
shopping 1991, September 5367 5320 Chichester
shopping 1991, December 4949 4960 Chichester
shopping 1992, March 5298 5467 Chichester
shopping 1992, November 5199 5092 Chichester
shopping 1990, July 4141 4389 Horsham
shopping 1991, September 3674 3660 Horsham
shopping 1991, December 3707 3822 Horsham
shopping 1992, March 3633 3730 Horsham
shopping 1992, November 3688 3615 Horsham
shopping 1990, July 4266 4532 East Grinstead
shopping 1991, September 3954 3964 East Grinstead
shopping 1991, December 4028 3926 East Grinstead
shopping 1992, March 3689 3692 East Grinstead
shopping 1992, November 3920 3853 East Grinstead
shopping 1990, July 7138 6836 Lewisham
shopping 1991, September 6568 6363 Lewisham
shopping 1991, December 6514 6555 Lewisham
shopping 1992, March 6115 6412 Lewisham
shopping 1992, November 5325 6099 Lewisham
shopping 1990, July 6502 6648 Nine Elms
shopping 1991, September 6416 6398 Nine Elms
shopping 1991, December 6422 6503 Nine Elms
shopping 1992, March 6748 6716 Nine Elms
shopping 1992, November 7023 7057 Nine Elms
shopping 1990, July 4083 4277 Crystal Palace
shopping 1991, September 4107 4334 Crystal Palace
shopping 1991, December 4168 4050 Crystal Palace
shopping 1992, March 4174 4198 Crystal Palace
shopping 1992, November 4079 4105 Crystal Palace

We're going to do the exact same thing as in part a: use a two-sample t-test to compare the mean number of people shopping on the 6th of the month and the 13th of the month.

The alternative hypothesis is that there are more shoppers on the 13th than on the 6th, and the null hypothesis is that the number of shoppers on the 13th is less than or equal to the number on the 6th. We will be using a one-sided test.

If you calculate the mean and standard deviations of the data (you should get mean = 4971, sd = 1166 for the 6th and mean = 5017 and sd = 1173 for the 13th) and calculate the test statistic, you will get t = -0.189. If you compare this to a t-distribution with 88 degrees of freedom, you will find that the means of the two groups are NOT significant (p = 0.425).

Therefore, there is NOT evidence that more people shop on Fridays the 13th.