Math 110 Chapter 3 StatCrunch Assignment

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LMC Statistics Math 110 Name: Naima Saleh StatCrunch Assignment Chapter 3 Math 110 Titanic Passenger List Data Set Part 1: Two-way contingency table You will be using the Math 110 Titanic Passenger List data file in StatCrunch. To find the data file, choose Explore -> Data. In the search box in the upper left, type “Math 110 Titanic” and click search. Click to open the data file. You can save the file to “my data” by clicking Data -> Save. 1. There are 16 variables in the data set, corresponding to the 16 columns in the data matrix/ spreadsheet (you can ignore the State Continued column). Note that the variable “survived” is coded so that 0 indicates the passenger did not survive and 1 indicates the passenger survived. List the categorical variables here: last name, first name, siblings and spouses, parents and children, boat number, home destination, home state, class, survived, sex, age 2. You will construct a two-way contingency table to analyze the relationship between passenger class and survival. Select Stat -> Tables -> Contingency -> With Data. For the row variable, choose pclass (passenger class) and for the column variable select survived. Click compute. The contingency table is the top result, for now you can ignore the Chi-Square results. Record your results in this table: Did not survive 0 Survived 1 Total 1 st class 123 200 323 2 nd class 158 119 277 3 rd class 528 181 709 Total 809 500 1309

LMC Statistics Math 110 3. Using your table, calculate and compare the probability that a passenger survived given they were a 1 st class passenger with the probability that a passenger survived given they were a 3 rd class passenger. Write a clear sentence explaining whether or not there is a relationship between passenger class and survival on the Titanic. The probability of people that survived the Titanic being in the 1st class was about 61.9% and only 25.5% of people in 3rd class meaning the higher the passenger class the higher chance you were able to survive the Titanic. 4. What is the marginal probability that a passenger survived the Titanic? How does this compare to the probability that a passenger survived given they were a 1 st class passenger? 500/1309 = 38.2% chance that a passenger survived the Titanic, 61% of the 1st class passengers survived meaning your chance of survival was highly increased if you were in the 1st class passenger. 5. What is the joint probability that a passenger survived and they were a 2 nd class passenger? Compare this to the joint probability that a passenger survived and they were a 3 rd class passenger. Why would it be wrong to use these probabilities to claim that 2 nd class passengers survived at a lower rate than third class passengers? 2nd class passenger probability= 0.0909 = 9.0% 3rd class passenger probability = 0.1383 = 13.8% The overall number of how many people were in each class passengers is not calculated in this probability so it wouldn't be a proven claim. 6. Calculate the conditional probability that a passenger survived given they were a 2 nd class passenger, and compare to your earlier calculation of the conditional probability that a passenger survived given they were a 3 rd class passenger. What can you conclude from these probabilities?

LMC Statistics Math 110 2nd class survival =0.238= 23.8% to the 13.8% of 3rd class passenger probability of survival. I can conclude that your chance of survival is higher if you were in the 2nd passenger class. Part 2: Probability distributions and the law of large numbers Return to the StatCrunch menu open in the first tab, and click Open StatCrunch to open a blank data matrix/ spreadsheet in a new tab. Select Applets -> Simulation -> Coin flipping. Click Compute without making any edits so that you get the default settings. The default settings assume the coin is fair, and the probability of heads is 0.5. A blank graph pops up. Make sure that Outcomes is clicked above the y-axis. 1. Click 1 run a few times and watch the simulation. Click 5 runs a few more times. Describe, insert graphs from StatCrunch, or give a sketch of the resulting bar graph in the space below. 2. Now click Convergence instead of Outcomes above the y-axis. Describe, insert graphs from StatCrunch, or give a sketch of the resulting scatter plot. The mathematical term convergence means that the scatter plot values get close to a specific value. What value does the scatter plot appear to converge to? The value that the scatter plot appears to converge to is 7

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