Final answer:
A proportion problem in statistics involves comparing categorical data to estimate population proportions and testing for differences. Hypothesis tests, such as z-tests for two proportions, and a comparison of p-values to the significance level determine whether there's a significant difference between the groups' proportions.
Step-by-step explanation:
When you're asked to test whether the proportions are equal for each category at a certain level of significance, you are dealing with a proportion problem in statistics. This refers to comparing categorical data where the outcomes fall into two categories, often framed as Success/Failure or Yes/No. In the context of proportion problems, you're interested in estimating the population proportion, which is the fraction of the population having a particular attribute, and testing if there is a statistically significant difference between proportions from different groups or at different times.
To determine if there is a difference between proportions, a hypothesis test such as the z-test for two proportions is used. The null hypothesis typically states that there is no difference between the population proportions, while the alternative hypothesis suggests that there is a difference. If the p-value calculated from the test statistic is less than the level of significance (alpha), the null hypothesis is rejected, indicating sufficient evidence of a difference in proportions.