Case study 1

A random sample of cars was taken and various measurements were recorded regarding the cars.

The data can be seen below.

##      type price mpgCity driveTrain passengers weight      MPG
## 1   small  15.9      25      front          5   2705 mpg < 23
## 2 midsize  33.9      18      front          5   3560 mpg < 23
## 3 midsize  37.7      19      front          6   3405 mpg < 23
## 4 midsize  30.0      22       rear          4   3640 mpg < 23
## 5 midsize  15.7      22      front          6   2880 mpg < 23
## 6   large  20.8      19      front          6   3470 mpg < 23

Afterwards, the data was condensed into a contingency table.

##          
##           mpg < 23 mpg >= 23
##   large         11         0
##   midsize       22         0
##   small         16         5

Suppose we were interested in knowing if there is a difference in gas mileage between small, midsize, and large cars.

  1. Calculate each of the following percentages:
  1. What is the percentage of all cars in the sample that had fuel economy greater than 23 mpg?
  2. Is there evidence to suggest that small cars get better gas mileage than large cars? Explain.

Case study 2

The following data was pulled from a college statistics class. 164 students had both their midterm grade and their class section number recorded. See the first ten students below.

##   Midterm1 Section
## 1       67       a
## 2       59       a
## 3      100       a
## 4       81       a
## 5       80       a
## 6       63       a

The data was then further condensed into a contingency table displaying the number of students in each section that passed or failed the midterm. See below.

##    
##     fail pass
##   a   22   36
##   b   25   30
##   c   12   39

Suppose we were interested in knowing whether there was a big difference in ‘pass rates’ between different class sections (the percent of students who passed the test).

  1. Calculate the pass rate for each of the three class sections.
  2. Is there a substantial difference in the pass rates between the classes? If so, how did you define ‘substantial’?
  3. What sorts of things might contribute to the difference between pass rates in these classes? Could it purely be due to random variability?

Would you gamble?

Let’s say I want to make a bet with you. I give you a 6 sided die and tell you that if you roll a ‘One’ you pay me $10. If you roll a ‘Four’, ‘Five’, or ‘Six’, I pay you $10. You suspect some funny business so you say you will only do it if I will first roll the dice 60 times and record the outcomes so you can look at the data. I agree and record the results below.

## draws
##  Five  Four   One   Six Three   Two 
##     6     8    16     9     9    12
  1. Calculate the percentage of times each of the six outcomes appears in the 60 draws.
  2. Based on the percentages we calculated, would you take my bet? Explain your reasoning.