Final answer:
To test the claim regarding the proportions of men and women owning cats, a Chi-square test should be used. This test is appropriate for comparing proportions in two categorical variables and determining if there is an association between them.
Step-by-step explanation:
To test the claim that the proportion of men who own cats is different from the proportion of women who own cats, given two independent samples of different sizes (150 men and 70 women), the appropriate statistical test is a Chi-square test for independence or homogeneity.
This is because we want to determine if there is an association between the two categorical variables - gender and pet ownership (owning cats in this case). A t-test is usually used to compare means from two samples, ANOVA is used to compare means across three or more samples, and regression analysis is used to predict the value of one variable based on the value of another. None of these apply in this situation as we are dealing with proportions and categorical data.
Steps to perform a Chi-square test:
- Set up the null hypothesis as there being no difference in cat ownership between men and women.
- Calculate the expected frequencies assuming the null hypothesis is true.
- Calculate the Chi-square statistic by summing the squared difference between observed and expected frequencies divided by the expected frequencies.
- Compare the statistic to the critical Chi-square value from the Chi-square distribution table at the desired level of significance to make a decision to accept or reject the null hypothesis.
Data like the one mentioned in the example: Men who own cats = 2/8, and the test for the proportion of homeowners between 2010 and 2011 in a Chi-square test for homogeneity, supports this approach.