5. a) Dr Anna is a psychologist at a counselling services center. She is interested to find out whether there are any differences in male-female students driving behaviors. She carried out a survey and collect the data on the fastest speed driven by student which is summarized as follows: Males n = 10 Females n = 20 x = 105.5 km/hour s = 20.1 km/hour x = 90.9 km/hour s = 12.2 km/hour Assuming that the fastest speed driven by student follows normal distribution, assess at a = 0.05 whether there is sufficient evidence to conclude that the standard deviation of the fastest speed driven by male college student differs from that of female college students. Answered (II Marks) b) An insurance company teams up with Dr Anna for a study on looking at the issue of female-male student drivers where they claim that female student drivers get into fewer accidents compared to male student drivers. Specifically, they say male student drivers are 65% held responsible for accidents while female student drivers are 35% responsible. In another study, it was found that 46 out of 85 drivers involve male student drivers. Use the Chi-Square Goodness of Fit test at a = 0.025 to verify the insurance company and Dr. Anna's claim based on the following hypotheses: H: Male student drivers are responsible 65% of accidents and female student drivers are responsible for 35% H: The data does not match the insurance company and Dr Anna's claim Not answered yet (9 Marks [Total: 20 Marks]