Chapter 13

  1. There is a difference between proof and evidence. Evidence suggests that there is a strong correlation between two things, but there is still room for doubt. Proof is considered to be undeniable and final. Proof is based on a massive set of evidence in order to support a conclusion. In the case of which bike path was quicker there are many conditions that could affect which is faster. If there were construction on the busy road the congestion would likely slow down the rider. There is also a smaller chance of disturbances on the backroads that could lead to the busy road being the slower route.

  2. The p-value tests the hypothesis of an experiment, not the data gathered from it. A p-value is just the probability that the null hypothesis is false. While the results of the experiment were found to have statistical significance the difference in the outcome does not have to be significant. It’s possible to have a p-value of 0.00000000001 with only a 1 second difference in time between the paths.

  3. Besides testing hypotheses statistics can be used to make predictions. Weather, sports, and elections can all be predicted (correctly or not) based on statistical models. These models are based on past occurences to predict an accurate outcome for the present or future.

Chapter 14

  1. The null hypothesis is used to determine the probability that the outcome occurred by chance. The alternative hypothesis is used to determine the probability that the outcome occurred by a non-random cause. The hypothesis given the data cannot be certain that one particular thing was the cause of the outcome. Multiple variables could have been the cause and it’s difficult to determine exactly the magnitude of effect of each variable.

2. b. African American males do not have a harder time than white males hailing a taxi in New York City.

c. Hospitals in New York State do not have higher than average Cesarean rates.
  
e. Patients taking a new, less toxic type of chemotherapy will not have response rates at least as good as those on the standard (and unpleasant) chemotherapy drug.

Chapter 15

  1. The significance of a p-value is not set in stone. The value of significance is determined by a person studying in a particular field. A p-value of 0.05 is based on the 2σ criterion (in this case σ represent standard deviation). In some fields like particle physics or manufacturing the certainty is based on the 5σ criterion, which corresponds to a p-value of about 1 in 3.5 million.

  2. The non-significant p-value in the Michael Jordan experiment comes from the small sample size. If each person had shot 7000 free throws and Jordan made all of them while the statistician made 3000 of them the p-value would be quite a bit smaller than 0.05.

  3. A p-value could be used in a criminal trial to assess the data. For example a p-value could provide the probability that a shoeprint found at a crime scene randomly matches any other given shoeprint. The p-value provides a way of assessing the reliability of the evidence presented in a criminal trial.