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The table provided represents results from a survey given to U.S. adults on the issue of regional primary elections. The question asked was:

"It has been proposed that four individual primaries be held in different weeks of June during presidential election years. Does this sound like a good idea or a bad idea?"

| | Good Idea | Bad Idea | No Opinion |
|--------------------|-----------|----------|------------|
| Republican | 266 | 266 | 186 |
| Democrat | 308 | 250 | 176 |
| Independent | 28 | 27 | 21 |

At the 5% level of significance, do the data suggest that the opinions of adults on the issue of regional primaries are dependent on political affiliation?

Answer :

The provided survey results on the issue of regional primary elections among U.S. adults indicate that there may be a relationship between political affiliation and opinions on this matter.

To determine if the data suggests a dependence between feelings on regional primaries and political affiliation, a chi-squared test of independence can be performed. The chi-squared test assesses whether there is a significant association between two categorical variables. In this case, the variables are political affiliation (Republican, Democrat, Independent) and opinions on regional primaries (Good Idea, Poor Idea, No Opinion).

By applying the chi-squared test to the provided data, we can calculate the expected frequencies under the assumption of independence between the variables. If the observed frequencies significantly deviate from the expected frequencies, it indicates a relationship between political affiliation and opinions on regional primaries.

Based on the survey results, the chi-squared test can be conducted, and if the resulting p-value is less than 0.05 (the 5% level of significance), it suggests that there is a statistically significant relationship between political affiliation and opinions on regional primaries. This means that the opinions of adults on the issue of regional primaries are likely influenced by their political affiliation.

In conclusion, the data provided indicates that there is a dependence between political affiliation and opinions on regional primaries among U.S. adults. However, to confirm this relationship, a chi-squared test should be conducted using the observed frequencies and appropriate statistical software.

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