Null hypothesis for a test of independence

Full Answer Section

  The conclusion for this test result would be that there is a significant association between color preference and number of siblings. This means that the probability of a person preferring a particular color is influenced by the number of siblings they have. For example, if the investigator found that people with more siblings were more likely to prefer the color blue, the conclusion would be that there is a positive association between color preference and number of siblings. This means that as the number of siblings increases, the probability of a person preferring blue also increases. 3. Explain the short cut method of calculating 2 and give a numerical example The short cut method of calculating 2 is a simplified version of the standard formula for calculating 2. The short cut method can be used when the expected frequencies in each cell are all equal. The formula for the short cut method is: For example, let's say that we have a sample of 100 people and we want to test the relationship between color preference and number of siblings. We have the following data: The expected frequencies for each cell would be 33.33, because 100 / 3 = 33.33. The 2 for this example would be: 4. Describe Phi and the odds ratio Phi (φ) is a measure of association between two categorical variables. It is a special case of the Pearson correlation coefficient, and it can be interpreted in the same way. Phi ranges from 0 to 1, where 0 indicates no association and 1 indicates perfect association. The odds ratio is another measure of association between two categorical variables. It is a ratio of the odds of one outcome occurring in one group to the odds of the same outcome occurring in another group. The odds ratio can be interpreted as the relative risk of one outcome occurring in one group compared to another group. For example, if the odds ratio for the relationship between color preference and number of siblings is 2, this means that the odds of a person with more siblings preferring blue are twice as high as the odds of a person with fewer siblings preferring blue. I hope this helps!

Sample Solution

  The null hypothesis for a test of independence is that there is no association between the two variables being tested. In other words, the null hypothesis states that the probability of observing a particular outcome in one variable is not influenced by the value of the other variable. For example, if we are testing the relationship between color preference and number of siblings, the null hypothesis would be that there is no association between these two variables. This means that the probability of a person preferring a particular color would be the same regardless of how many siblings they have.