Stat Homework 2 Write

Stat Homework 2 Write-Up Question 1:  The above scatterplot depicts the relationship between the IMDb rating and season number of Family Guy episodes. It is evident that earlier seasons tended to have higher ratings. To accurately describe the variability in the dataset, the mean and standard deviation would be the best measures due to the presence of outliers - some low-rated episodes in later seasons and high-rated episodes in earlier seasons. The maximum rating observed was 9.1/10 in Season 8, while the minimum was 4.1/10 in Season 17. The mean rating was calculated to be 7.1/10, with a standard deviation of 0.59. Prior to Season 10, only a few episodes fell below the mean rating, but between seasons 10-20, a substantial number of episodes fell below the mean in each season.

Question 2: P (stocks)= 0.36, P(futures)=0.22, P (stocks, futures) = 0.15 A. P (Futures | Stocks) a. P(Futures|Stocks) = P(Futures,Stocks)/ P(Stocks) b. P(Futures | Stocks) = 0.15/0.36 i. P(Futures | Stocks) = 0.42 B. P(Futures or Stocks) = P(Stocks) + P(futures) - P (stocks, futures) a. P(Futures or Stocks) = 0.36 + 0.22 -0.15 i. P(Futures or Stocks) = 0.43 C. P(Futures, No Stocks)= 0.07 Yes Futures No Futures Total Yes Stocks 0.15 0.21 0.36 No Stocks 0.07 Total 0.22 Question 3: Part A: A. P(use_sex)= TRUE a. 0.27 B. P(use_sex = TRUE | show_product_quickly = TRUE) a. 0.27 C. P(use_sex = TRUE | show_product_quickly = FALSE) a. 0.26 D. 27% of the Super Bowl ads in the sample used sex appeal. The probability of using sex appeal given that the product is shown quickly is 27%, which is the same as the overall probability of using sex appeal. This indicates that showing the product quickly does not affect the likelihood of using sex appeal in the ad and that the events are independent of each other. Part B: A. P(patriotic = TRUE) a. 0.17 B. P(patriotic = TRUE | celebrity = true) a. 0.17 C. P(patriotic = TRUE | celebrity = FALSE) a. 0.16 D. Based on the probabilities, it appears that there isn't a significant link between the use of celebrities and the inclusion of patriotic symbolism in the ads. In particular, the probability of using patriotic symbolism is the same (at 0.17) for both ads that feature celebrities and those that don't 0.17, so you can conclude that these events occur independently of each other. Part C: A. P(funny = TRUE) a. 0.69 B. P(funny = TRUE | danger = TRUE)

Part C  The density histogram shows that artwork created before 1950 and with a width less than 2000mm tended to be narrower compared to post-1950 artwork. Post- 1950 artwork showcases a wider range of widths and exhibits more variability in its width distribution. Part D  The medium with the largest maximum height is Steel with a maximum height of 37,500 millimeters.  Aluminum and Plexiglass have the smallest median heights both being 6 millimeters.  Rubber has the highest IQR height of 3825 millimeters.