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HW06-FSZT: Problem 8 Problem Value: 7 point(s). Problem Score: 0%. Attempts Remaining: 4 attempts. (7 points) 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 508 adults living in Lithuania. Of these, 428 were married and 80 were cohabitating 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 future. Responses to the survey are summarized in the table below. Household status Happy Optimistic |Not Happy Total Married 224 148 56 428 Cohabitating 37 29 14 80 Total 261 177 70 508 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. Ha: There is a relationship between happiness level and family status. 1. Which statistical test should Brigita use? O A. t test for sample mean OB. x2 test of independence OC. x2 goodness of fit test O D. Z test for one population proportion O E. Z test for difference of two population proportions 2. What conditions must be met for the hypothesis test to be valid? QA. There must be at least 3 levels of the categorical variable. OB. There must be an expected count of at least 5 for each cell in the table. [C. There must be at least 10 'success' and 10 'failure' observations. OD. Each observation must be independent of all other observations.Ha: There is a relationship between happiness level and family status. 1. Which statistical test should Brigita use? OA. t test for sample mean OB. X' test of independence Oc. x2 goodness of fit test O D. Z test for one population proportion OE. Z test for difference of two population proportions 2. What conditions must be met for the hypothesis test to be valid? OA. There must be at least 3 levels of the categorical variable. OB. There must be an expected count of at least 5 for each cell in the table. OC. There must be at least 10 'success' and 10 'failure' observations. OD. Each observation must be independent of all other observations. OE. Population data must be nearly normal or the sample size must be at least 30. 3. What is the degrees of freedom for this test? df 4. Under the null hypothesis model, what is the expected count for people who are Married and Optimistic? expected count = 5. Calculate the contribution to the test statistic for people who are Married and Optimistic. contribution = 6. Calculate the test statistic for this procedure. Help Entering Answers Preview My Answers Submit Answers