The results of a survey are shown in the table. The data shows the number of votes by fans for contestants on a popular television show. The observed counts are: Contestant A: 142, B: 120, C: 138. Which test is used to determine if the data is significantly different than expectations?
A goodness-of-fit test
A goodness-of-fit test is used to determine if the observed data significantly deviates from the expected distribution. In this scenario, we are comparing the observed vote counts for contestants to see if they align with what we would expect under a certain hypothesis.
This test is designed to examine the relationship between two categorical variables to see if they are independent of each other. In this case, we are not assessing the relationship between variables but rather comparing observed counts to expected values for a single variable, making this test inappropriate.
This test evaluates whether different populations have the same distribution across categories. While it involves multiple groups, the situation here focuses solely on the observed votes for contestants, which does not involve comparing distributions across different populations.
A Student's t-test is used to compare the means of two groups to determine if they are statistically different from each other. Since the data involves categorical counts rather than continuous variables, this test does not apply to the given voting scenario.
To assess whether the observed voting data for contestants significantly differs from the expected counts based on a hypothesized distribution, a goodness-of-fit test is the appropriate choice. This test specifically evaluates how well the observed data matches the expected outcomes, making it the best fit for this analysis of contest results.
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