this question:

You will need this table in the problem. Below is a. table of x2 critical values. 0.25 0.2 0.15 0.1 0.05 0.01 0.001 df 1 1.323 1.642 2.072 2.706 3.841 6.635 10.828 2 2.773 3.219 3.794 4.605 5.991 9.210 13.816 3 4.108 4.642 5.317 6.251 7.815 11.345 16.266 4 5.385 5.989 6.745 7.779 9.488 13.277 18.467 5 6.626 7.289 8.115 9.236 11.070 15.086 20.515 6 7.841 8.558 9.446 10.645 12.592 16.812 22.458 7 9.037 9.803 10.748 12.017 14.067 18.475 24.322 8 10.219 11.030 12.027 13.362 15.507 20.090 26.124 9 11.389 12.242 13.288 14.684 16.919 21.666 27.877 10 12.549 13.442 14.534 15.987 18.307 23.209 29.588 **************************************************************************************** Data were collected at a movie theater's snack bar about what customers purchased. In addition, it was noted if the customer was a Child (age 12 and under), Student (had a student ID) or an Adult (over age 12 and no student ID). The table below indicates the results of the survey. Write probability statements where appropriate. Purchases at Snack Bar . POPCORN OTHER ITEM Multiple Movue patron ONLY ONLY Items 3 14 27 Answer the questions below on your own paper. Clearly label each part of the question and SHOW WORK where requested. Answer the questions below on your own paper. Clearly label each part of the question and SHOW WORK where requested. a) What is the probability that a customer purchased multiple items? Is this a joint, conditional, or marginal probability? SHOW WORK! (3 points) b) Write out the Null Hypothesis and the Alternative Hypothesis for a Chi-Square (X2) test to determine whether there is a relationship between the movie patron Status and the type of snack(s) purchased. (2 points) c) Below is a table of expected counts. Calculate the expected cell counts for the two missing cells (highlighted in yellow). SHOW WORK (3 points) Purchases at Snack Bar POPCORN OTHER ITEM Multiple ONLY ONLY Items Child 7.8558 3.1058 Movie patron Student 7.1923 18.6154 m 16.9519 17.3462 d) Below is a table of partial 2 values. Calculate the partial 2values for the two missing cells (highlighted in yellow). SHOW WORK (3 points) Purchases at Snack Bar POPCORN OTHER ITEM Multiple Movie patron ONLY ONLY Items Child 2.1862 3.1581 Student 0.7970 0.0907 1.1443 Adult 3.7301 0.4322 e) What is the value of the 2 test statistic? SHOW WORK (2 points) f) Use a = 0.05. What are the degrees of freedom for the test and the 2critical (i.e. table) value? (2 points) g) Write out your conclusion to the Chi-square ( ) test in terms of the story. Give the reasoning behind your conclusion. (3 points)