11.3.2.1 - Example: Raw Data

Example: Dog & Cat Ownership Section

Is there a relationship between dog and cat ownership in the population of all World Campus STAT 200 students? Let's conduct an hypothesis test using the dataset: fall2016stdata.mpx

1. Check any necessary assumptions and write null and alternative hypotheses.

 \(H_0:\) There is not a relationship between dog ownership and cat ownership in the population of all World Campus STAT 200 students
\(H_a:\) There is a relationship between dog ownership and cat ownership in the population of all World Campus STAT 200 students

Assumption: All expected counts are at least 5. The expected counts here are 176.02, 75.98, 189.98, and 82.02, so this assumption has been met.

2. Calculate an appropriate test statistic.

Let's use Minitab to calculate the test statistic and p-value.

  1. After entering the data, select Stat > Tables > Cross Tabulation and Chi-Square
  2. Enter Dog in the Rows box
  3. Enter Cat in the Columns box
  4. Select the Chi-Square button and in the new window check the box for the Chi-square test and Expected cell counts
  5. Click OK and OK
Rows: Dog Columns: Cat
  No Yes All
No 183 69 252
  176.02 75.98  
Yes 183 89 272
  189.98 82.02  
Missing 1 0  
All 366 158 524
Chi-Square Test
  Chi-Square DF P-Value
Pearson 1.771 1 0.183
Likelihood Ratio 1.775 1 0.183

Since the assumption was met in step 1, we can use the Pearson chi-square test statistic.

\(Pearson\;\chi^2 = 1.771\)

3. Determine a p value associated with the test statistic.

\(p = 0.183\)

4. Decide between the null and alternative hypotheses.

Our p value is greater than the standard 0.05 alpha level, so we fail to reject the null hypothesis.

5. State a "real world" conclusion.

There is not evidence of a relationship between dog ownership and cat ownership in the population of all World Campus STAT 200 students.