Question

A variable contains four categories. It is expected that data are uniformly distributed across these four categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21. Using a = .05, the observed chi-square value is 2. b) Using a = .05, the critical chi-square value is What is the conclusion of the test ? Answer:

Answer 1

To test the uniform distribution of data across four categories, a chi-square test for goodness-of-fit can be conducted. The observed frequencies are compared to the expected frequencies, but the expected frequencies are not provided. The conclusion of the test depends on comparing the observed chi-square value to the critical chi-square value at a significance level of 0.05.

Step-by-step explanation:

To test whether data are uniformly distributed across four categories, a chi-square test for goodness-of-fit can be conducted. The observed frequencies of 22, 35, 32, and 21 are compared to the expected frequencies under the assumption of a uniform distribution. However, it is not clear from the given information what the expected frequencies are for each category.

To find the critical chi-square value at a significance level of 0.05, you need to know the degrees of freedom. This can be calculated as (number of categories - 1). In this case, df = 4 - 1 = 3. You can refer to a chi-square distribution table or use statistical software to find the critical value.

The conclusion of the test depends on comparing the observed chi-square value (2) to the critical chi-square value. If the observed value is less than the critical value, we fail to reject the null hypothesis of a uniform distribution. If the observed value is greater than or equal to the critical value, we reject the null hypothesis and conclude that the data are not uniformly distributed.