Chapter 13:
1) To say you have proved something suggests that it is a fact. He did not prove that the busy road was ALWAYS the fastest, but the evidence suggested that in most cases the busy road was quicker than the back roads.
2) A p-value isn’t a numbers that shows the amount of difference between two things. P-values are used to test the hypotheses; the resulting number indicates that there is a difference between whatever is being tested, but it doesn’t mean that it is a large amount of difference. In this case, the travel times between the two routes was slight, however the small p-value indicated that one route was still faster than the other.
3) You can use statistics in a variety of fields. Educators use them all the time to look at how their students progress throughout the year and within a certain subject. The pattern and trends that teachers look at can indicate gifted and talented students as well as the students with learning disabilities. Other fields that use statistics would be forensics (woo CSAFE), almost every form of research, marketing, etc.
Chapter 14:
1) “The probability of the data under the null hypothesis” says we are trying to test whether or not the data will contradict what our null hypothesis is trying to tell us. When saying “the probability of the hypothesis given our data”, we are going purely based off the data we collected. The multiple variables that affected our data are not accounted for and neither is the significance of each variable.
2b) Null: African American men do not have a harder time than white men hailing a cab in NYC.
2c) Null: Hospitals in New York State do not have a higher than average rate of c-sections.
2e) Patients taking the new chemotherapy drug will not have response rates at least as good as the standard.
Chapter 15:
I think that if the p-value that is calculated is .049999 or .050001, the test needs to be ran again. These values are just too close to the cut off point to be considered significant or insignificant in a study. How far you round is crucial in these cases as well. If we were to round either of these to the hundred thousandth of a place, then these would both become .05 exactly. It is just too close to classify this number as significant or insignificant. 2) The sample size was too small for the data to be valid. If the sample size was at least 30, then maybe the p-value calculated could have been more valid.
3) A p-value is a number that allows you to refute or accept the null hypothesis. In criminal cases, the null hypothesis is always innocent. If you get a p-value that is less than .05, you reject the null hypothesis and accept the alternative, in this case, the criminal is not innocent. It is important to keep in mind that this is not an official yes or no answer, but a mere statistical tool that suggests he/she is not innocent.