In the early 1990's, researchers in the UK collected data on the number of traffic accident related emergency room (ER) admissions on Friday the 13th with the goal of addressing issues of how superstitions regarding Friday the 13th affect human behavior and and whether Friday the 13th is an unlucky day. The histograms below show the distributions of numbers of ER admissions at a sample of emergency rooms on Friday the 6th and Friday the 13th. For each ER, we have a pair of measurements, the number of admissions on the 6th and the number of admissions on the 13th. The table below provides some sample statistics, where the difference (last row) is the ER admissions on the 6th minus the ER admissions on the 13th: n Mean SD Friday the 6th 6 8 3 Friday the 13th 6 11 4 Difference 6 -3 3 sixth thirteenth diff 2.0 3 2.0 1.5 1.5 2 Count 1.0 1.0 0.5 0.5 0.0 0.0 5.0 7.5 10.0 12 16 -5.0 -2.5 0.0 Number of traffic accident related ER admissions For the questions below, use a mathematical model. The online T distribution calculator will prove useful (https://shiny.rit.albany.edu/stat/tdist/). Round your answers to 3 decimal places as necessary.For the questions below. use a mathematical model. The online T distribution calculator will prove useful [hjpsn'i'shinvi'it.albany.eclui'stati'tclisti'}. Round your answers to 3 decimal places as necessary. a. What is the standard error of the differences? b. The null hypothesis says that the average difference is zero. Using these data. find the corresponding T score. c. How many degrees of freedom are there? d. The alternative hypothesis says that the average difference is not equal to zero. Use the T score you found in part (b) to find the p value. e. Using a significance level of your choice. form a conclusion about whether accident admissions differ between Friday the Eith and Friday the 13th