Example 1: Helium Filled Footballs

football = read.csv("http://people.hsc.edu/faculty-staff/blins/StatsExamples/football.txt")
head(football)
##   Trial Air Helium difference
## 1     1  25     25          0
## 2     2  23     16         -7
## 3     3  18     25          7
## 4     4  16     14         -2
## 5     5  35     23        -12
## 6     6  15     29         14

Some people believe that footballs filled with helium will travel farther than regular footballs when kicked. The Columbus Dispatch did an experiment to find out. Two identical footballs were tested, one filled with helium, the other with ordinary air. A novice kicker punted the two balls several times without knowing which ball was which. In total, each ball was kicked 39 times and the distance travelled was measured in yards. The results are in the data frame football.

  1. How much farther did the helium filled football travel, on average?

  2. Is this a significant difference? Use the t.test() function to find out.

  3. What were the null and alternative hypotheses?

Example 2: Marriage Ages

marriages = read.csv("http://people.hsc.edu/faculty-staff/blins/StatsExamples/marriageAges.txt")
head(marriages)
##   husb wife
## 1   25   22
## 2   25   32
## 3   51   50
## 4   25   25
## 5   38   33
## 6   30   27

The data frame marriages contains data from 24 couples that were married in Cumberland county Pennsylvania one month. Assume for now that these couples are representative of couples throughout the United States.

  1. Who or what are the individuals in this data frame?

  2. On average, who is older, the husband or the wife? What is the average age gap?

  3. Make a histogram to show the distribution of the age gap. Would you say it is roughly normal?

  4. Are husbands significantly older than their wives, on average? Use the t.test() function to find out.

  5. What are the correct null and alternative hypotheses for this situation?

  6. Use the formula \(\displaystyle \bar{x} \pm t^* \sqrt{s^2 + \frac{s^2}{N}}\) to make a prediction interval for the age difference of 80% of all couples.