A recent survey of Austrian high school students asked whether it makes sense for 16-year-olds to be allowed to vote in the next parliamentary election. The following table shows results.

a. Verify, using software, that X² = 14.1 for this table.
b. Can you use the chi-squared distribution to find a P-value for testing whether an association exists between the grade level and the opinion on voting with 16? Why or why not?

c. Enter the data in the Permutation Test for Independence web app. Press the Generate Random Permutation(s) button once to generate one random permutation of the data. Did this permutation lead to a chi-squared test statistic smaller, equal, or larger than the observed value?
d. Press the button 9 more times. How many of the 10 permutations you generated resulted in a X² value as large or large than the observed? (The subtitle of the plot shows this information.)
e. Generate 10,000 permutations and find the permutation P-value. Interpret it.

Transcribed Image Text:

Voting with 16 Makes Sense Definitely Probably Probably not Definitely not Grade Sophomores Juniors 16 Seniors 12 5 3 3 20