1. The Differences in Ticket Prices for Broadway Shows By Courtney Snow I wanted to find out whether there was a significant difference in the price of musicals, plays, and musical revivals. The first thing I did was find the ticket prices for all of the 27 current Broadway shows, using broadway.com. In some cases, a range was given, and in other cases a single number was given. In order to make the numbers work together for an accurate analysis, I averaged those ticket prices that had a range, coming up with a single digit for each show. The descriptive statistics for the data are below. Descriptive Statistics: ticket price Variable N Mean Median TrMean StDev ticket p 28 83.18 81.25 83.33 11.20 Variable SE Mean Minimum Maximum Q1 Q3 ticket p 2.12 62.50 100.00 75.63 94.38 Next, I divided the ticket prices into categories according to the type of show it was, either a musical, a play, or a revival musical. Below are the descriptive statistics for all three categories. Descriptive Statistics: ticket price_musical Variable N Mean Median TrMean StDev SE Mean ticket p 16 86.42 87.50 86.98 11.00 2.75 Variable Minimum Maximum Q1 Q3 ticket p 65.00 100.00 80.00 95.00 Descriptive Statistics: ticket price_play Variable N Mean Median TrMean StDev SE Mean ticket p 5 72.50 75.00 72.50 6.61 2.96 Variable Minimum Maximum Q1 Q3 ticket p 62.50 80.00 66.25 77.50 Descriptive Statistics: ticket price_revival musical Variable N Mean Median TrMean StDev SE Mean ticket p 6 86.04 83.13 86.04 8.53 3.48 Variable Minimum Maximum Q1 Q3 ticket p 77.50 100.00 79.38 94.38 After looking at this data, I decided to use two- sample t-tests to find out if there was a significant difference between the three types of shows. The results of these tests are below. Two-Sample T-Test and CI: ticket price-play, ticket price-musical Two-sample T for ticket price-play vs ticket price-musical N Mean StDev SE Mean ticket p 5 72.50 6.61 3.0 ticket p 16 86.4 11.0 2.8 Difference = mu ticket price-play - mu ticket price-musical Estimate for difference: -13.92 95% CI for difference: (-22.81, -5.03) T-Test of difference = 0 (vs not =): T-Value = -3.45 P-Value = 0.005 DF = 11 Two-Sample T-Test and CI: ticket price-play, ticket price-revival musical Two-sample T for ticket price-play vs ticket price-revival musical N Mean StDev SE Mean ticket p 5 72.50 6.61 3.0 ticket p 6 86.04 8.53 3.5 Difference = mu ticket price-play - mu ticket price-revival musical Estimate for difference: -13.54 95% CI for difference: (-24.08, -3.01) T-Test of difference = 0 (vs not =): T-Value = -2.96 P-Value = 0.018 DF = 8 Two-Sample T-Test and CI: ticket price-musical, ticket price-revival musical Two-sample T for ticket price-musical vs ticket price-revival musical N Mean StDev SE Mean ticket p 16 86.4 11.0 2.8 ticket p 6 86.04 8.53 3.5 Difference = mu ticket price-musical - mu ticket price-revival musical Estimate for difference: 0.38 95% CI for difference: (-9.39, 10.15) T-Test of difference = 0 (vs not =): T-Value = 0.09 P-Value = 0.933 DF = 11 Analysis: From the two-sample t-tests, I was able to conclude if the differences in ticket price were statistically significant. In the case of the price to see a play compared to the price to see a musical, the p-value is 0.005, so it is significant at the 0.05 level. Therefore, there is a statistical difference between the prices of a play and a musical. In the next set of data, the comparison of the price of a play to the price of a revival musical, the p-value is 0.018. So, there is a significant difference between the two types of shows. In the final comparison, between the ticket price of a musical and a revival musical, I did not find any significant value to conclude that there is in fact a difference between the two prices. The p- value was 0.933, and the confidence interval contained the number zero, not letting me reject the null hypothesis that there is no difference between the two. Overall, plays are less expensive than musicals or musical revivals. So, depending on what show you want to see, you will pay a different price. For the graphical displays, I decided to use three dotplots, each showing the frequency of various prices.