a Happy households - Changes in family structure have occurred rapidly in the Eastern European country of Lithuania in recent years. Social scientists are interested in whether a person's self-described level of happiness depends upon their family status. Brigita is part of a research team that surveyed a random sample of 594 adults living in Lithuania. Of theso, 476 were married and 118 were divorced. The team asked the survey respondents to evaluate their happiness level over the past year and to imagine how happy they expected to be in the next 5 years. They grouped the responses into three categories: Happy: In the previous year they were happy and expect to be happy in the next 5 years. Optimistic: In the previous year they were unhappy but expect positive changes in the next 5 years. Not Happy. In the previous year they were unhappy and do not expect that to change in the futuro Responses to the survey are summarized in the table below. Household status Happy Optimistic Not Happy Total Married 249 165 62 476 Divorced 45 48 25 118 Total 294 213 87 594 Round all calculated answers to 4 decimal places where appropriate Brigita wants to conduct a hypothesis test using the hypotheses Ho: There is no relationship between happiness level and family status H. There is a relationship between happiness level and family status 1. Which statistical test should Brigita use? A Z test for one population proportion B. x? test of independence c. 2 test for difference of two population proportions D. t test for sample mean Ex? goodness of fittest 2. What conditions must be met for the hypothesis test to be valid? A. There must be at least 3 levels of the categorical variable. B. There must be an expected count of at least 5 for each cell in the table. C. Each observation must be independent of all other observations. D. Population data must be nearly normal or the sample size must be at least 30. E. There must be at least 10 success' and 10 failure' observations. 3. What is the degrees of freedom for this test? ODOC df = 4. Under the null hypothesis model, what is the expected count for people who are Married and Happy? expected count = 5. Calculate the contribution to the test statistic for people who are Married and Happy. contribution- 6. Calculate the test statistic for this procedure