11.3.2.1 - Video Example: Dog & Cat Ownership (Raw Data)

This example uses the dataset:

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

Cell contents grouped by No, Yes, Missing; First row: count, Next row: expected count

Rows: Dog | Columns: Cat
  No Yes All
BaNock 183 69 252
  176.02 75.98  
Yes 183 89 272
  189.98 82.02  
Missing 1 0  
All 366 158 524

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.
Chi-Square Test
  Chi-Square DF P-Value
Pearson 1.77 1 0.1833
Likelihood Ratio 1.77 1 0.1828

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

\(Pearson\;\chi^2 = 1.77\)

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

\(p = 0.1833\)

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.