GROUP TASK #16: Chi-Square Tests - ANSWERS
In a survey of orchestral works it was found that 70 percent include an oboe as part of the orchestration. A music scholar finds that composer A uses an oboe in only 10 of 22 orchestral works (just 45%). Is this a statistically significant difference?
70 percent of 22 works is 15.4 works 30 percent of 22 works is 6.6 works 
With one degree of freedom, at the 95% confidence level, the critical value of chi-square is 3.84. Since our calculated chi-squared value exceeds the critical value, we can declare that the results are not consistent with the null hypothesis. Instead, the results are consistent with the research hypothesis.
Our statistical test allows us to state the following conclusion: The observations are consistent with the idea that, compared with other composers, composer A is less likely to include an oboe in the instrumentation of orchestral works.
A music scholar finds that a sample of Italian baroque music shows 51 works in major keys and 9 works in minor keys. In a diverse sample of baroque music from many European countries (including Italy), 480 works were found to be in major keys and 210 works in minor keys. Compared with their European colleagues, did Italian baroque composers tend to favor works in major keys?
210 (minor) + 480 (major) works = 690 works in total 210/690 = 30.4348 percent minor 480/690 = 69.5652 percent major For a sample of 60 Italian baroque works, we would expect: 30.4348 percent of 60 = 18.2609 in the minor mode 69.5652 percent of 60 = 41.7391 in the major mode 
With one degree of freedom, at the 95% confidence level, the critical value of chi-square is 3.84. Since our calculated chi-square value exceeds the critical value, we can discard the null hypothesis, and accept that the results are consistent with the hypothesis. The results are statistical significant at p<0.05.
Our statistical test allows us to state the following conclusion: The observations are consistent with the idea that, compared with other European baroque composers, Italian baroque composers tend to favor works in major keys.
An ethnomusicologist finds that just 130 of 220 Xhosa listeners say they prefer bumbuju rhythms to nobuju rhythms. In one Xhosa village however, 15 of 19 people say they prefer bumbuju. Can we claim that the members of this village differ significantly from other Xhosa in their rhythmic preferences?
130/220 Xhosa prefer bumbuju = 59.0909 percent 220-130 = 90; 90/220 Xhosa prefer nobuju = 40.9091 percent In the village, we would expect: 59.0909 % of 19 = 11.2273 to prefer bumbuju 40.9091 % of 19 = 7.77273 to prefer nobuju 
With one degree of freedom, at the 95% confidence level, the critical value of chi-square is 3.84. Since our calculated chi-square value fails to reach the critical value, we cannot discard the null hypothesis. The results are not consistent with the hypothesis.