MODULE 10 - Chi-Square Test of Independence - Lab AEC 505 - Statistical Methods in Agriculture Instructor: Dr. Jose Lopez Make sure you submit all your answers to this lab in one Word document. 1) A survey of 50 randomly selected students who drop a course in the current semester was conducted at a community college. The goal of the survey was to learn why students drop courses. The following data were collected: "Personal" drop reasons include financial, transportation, family issues, health issues, and lack of child care. "Course" drop reasons include reducing one's load, being unprepared for the course, the course was not what was expected, dissatisfaction with teaching, and not getting the desired grade. "Work" drop reasons include an increase in hours, a change in shift, and obtaining full-time employment. The results of the survey are as follows: Gender Drop Reason Gender Drop Reason Male Personal Male Work Female Personal Male Work Male Work Female Course Male Personal Male Work Male Course Female Course Male Course Female Course Female Course Female Course Female Course Male Work Male Course Male Personal Female Course Male Course Male Personal Female Course Male Work Female Course Male Work Male Course Male Course Female Course Male Course Male Work Male Work Male Course Page 1 of 4Sum = ? f. What is your final answer for the test statistic for the appropriate hypothesis? Need to carry at least four decimals in all your calculations to get the correct final answer. (Points: 10) g. What is (are) the critical value(s) for this hypothesis test? Use a = 0.10 significance level. (Points: 10) h. Do you reject or fail to reject Ho? Make sure you explain why. (Points: 10) i. State the correct conclusion (" There is sufficient evidence at the a = 0.10 significance level to support..." or "There is NOT sufficient evidence at the a = 0.10 significance level to support..."). Make sure you state the conclusion in terms of Hi. (Points: 10) j. Use Microsoft Excel to compute the P-value for the hypothesis test that gender is independent of drop reason. What is your P-value estimate? Hint: You need to use Tables 1 and 2 above and program in a cell in Excel the formula =CHISQ.TEST(actual_range,expected_range) (Points: 10) Page 4 of 4Female Personal Female Work Male Course Male Personal Female Work Male Work Male Work Female Course Male Work Male Course Female Course Male Personal Female Personal Female Course Female Personal Female Work Female Personal Male Work Is gender independent of drop reason at the a = 0.10 level of significance? a. State the null and alternative hypotheses. (Points: 10) HO: Gender is independent of reason for dropping a course . HI: Gender is not independent of reason for dropping a course b. Summarize the results of the survey in the contingency table below (Table 1). Hint: Copy and paste the raw data above into Microsoft Excel. Make sure you stack the data into two columns. Then, use the Filter feature of Microsoft Excel to separate the observations by gender and drop reason. That is, select the variables gender and drop reason, then click on the Data tab in the menu bar at the top of the window, then click on the Filter button. Once the filter drop down arrow boxes display, you can proceed to filter the observations as needed and summarize the results in Table 1 below. (Points: 10) Table 1. Results of the survey. Drop Reason Gender Total Personal Work Course Female 3 13 21 Male 6 13 10 29 Total 11 16 23 50 Page 2 of 4row total x column total c. Use Table 1 above and the formula E, = to compute the table total expected counts. Summarize your results in Table 2 below. Make sure you carry at least four decimals in all your calculations. (Points: 10) Table 2. Expected Counts Drop Reason Gender Personal Work Course Female 2.1000 1.2600 5.4600 Male 3.4800 7.5400 5.8000 d. Use the insert equation button from Microsoft Word to type the formula(s) for calculating the test statistic. Click on the Insert tab, then click on the Equation button, then use the Structures buttons and the Symbols buttons from the Equation Tools Design tab to type your formula. (Points: 10) . X = _ (0 - E)/E e. Use Table 3 below to compute the test statistic. Hint: Fill out the table in Microsoft Excel and then copy and paste the table into your Word document. Alternatively, you can fill out the table in Microsoft Excel and then copy and paste the values into the table below. (Points: 10) Table 3. Test Statistic Calculation. E O - E (0 - E) (0) - E) / E Page 3 of 4