Happy in Your Marriage? The General Social Survey asks questio...

Question

Happy in Your Marriage? The General Social Survey asks questions about one’s happiness in marriage. Is there an association between gender and happiness in marriage? Use the data in the table to determine if gender is associated with happiness in marriage. Treat gender as the explanatory variable.

Table showing counts of males and females categorized by levels of happiness in marriage: very happy, pretty happy, and not too happy.

Accepted Answer

A university wants to know if there's an association between a student's major, STEM, or humanities, and their preference for online or in-person classes. The data collected is shown below. We're given a table with major and the class preference. Is there an association between the student major and their class preference? Use a significance level of 0.05. We have two possible answers, being there is no association, or there is an association. Now, to solve this, let's first write our hypotheses. Our no is that there is no association. And our alternative is that there is an association. Now, we can perform Achi square test to solve this. We first need to find our expected values. So our expected value. Is given by the road total. Multiplied by the column total. Divided by the grand total. So, in our table, we can find our totals. For the online column, our total is 90, and the in-person column total is 110. For the stem column, our total is 100, and the Mandy's column, our total is also 100, giving us a grand total of 200. Now we can find our respected values. So we'll make a table here. With online? In person Stem And humanities For SEM and online, we have 90, multiplied by 100, divided by 200. For sim and in person. We have 110 multiplied by 100, divided by 200. For online humanities. We have 90, multiplied by 100. Divided by 200 And in person humanities. We have 110 multiplied by 100, divided by 200. We now get the following table. Or STEM in online, we get 45, SEM in person, we get 55. Humanities online, 45. And he manage in person, 55. We now have our expected values. We can now find our chi squared test statistic. This is given by the sum of our observed minus expected values squared divided by the expected values. Now, we have 60 minus 45, all squared divided by 45 for our STEM and online. For our standing person, we have 40 minus 55 squared divided by 55. For online humanities. We have 30 minus 45 squad. Divided by 45. And finally, for humanities in person, we have 70 minus 55 squared divided by 55. Now we can compute this in the calculator and sum everything together, which gives us a value of 18.2. Now that we have our test statistic, we can compare this to our critical value for chi squared. We first need degrees of freedom, which is just the number of rows, multiplied by the number of columns, both minus 1. We get 2 minus 1, multiplied by 2 minus 1, which is just 1. Now, the chi square critical, for an alpha of 0.05, degrees of freedom of 1 can be found with a table. And this value is 3.841. We can check our hypothesesis by seeing if our value is greater than the critical value, which it is. Because this is the case, we will reject our null hypothesis. We can then say, That there is an association between the student's major and their class preference, which means our answer is answer B. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

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