 Hi, this is Dr. Don and I have a problem out of McClave Chapter 3 and this has to do with conditional probabilities. We're given a table of summary data here about two types of meals, lunch and dinner, and whether or not patrons rated the service good or poor. This is a total of 133 and you can see they've given you the column totals down here and the row totals here and the grand total here which is good if you're trying to do this with a manual calculator but if you're trying to do it using stat crunch it adds a little bit of complexity. So let's see the first question is given that the meal was a dinner what is the probability that service was poor? The way to think about this if we look over here dinner is a row so we need the row values here and we want to know given if it's dinner given gives you the clue that that is the assumption the conditional and the probability that service is poor. So let's jump into stat crunch remember we can go to the little rectangle there click on copy the table and we'll open in stat crunch. Okay we've got stat crunch open and here's the problem that we have for some reason when they designed this particular problem in my stat lab they included these row and column totals and that confuses stat crunch. So the first thing you need to do is to highlight those and use control X to delete those totals and then I'm going to highlight this column and then use control X to delete that. Now we have just the information stat crunch can use and not get confused. So we go to stat look down until we find tables and then we go to contingency with summary our columns are the service good and service poor and then our row labels are the meals and we're going to go ahead and select the row percent hold down the control key hit the column percent and the percent of total and I'm going to go ahead and leave everything else standard and just click compute. So we get a table here a contingency table that we can use to answer our questions and it looks complex and confusing but if you remember what I told you the first question is given that the meal was a dinner so we look for dinner that's in a row you can see the row is highlighted there and we want to know what is there probably the service was poor so we look in the poor column but we're in the dinner row we look up here in this legend you can see that the first number in parentheses is the row percent the second is the column percent and the third is percent of total. So we go down here in our dinner row we go to the service poor column and we want the row percent and that's sixty one point five four percent and remember we need to change that back to a decimal so it'd be point six one five which is the answer over here. The second question is if the respondent gives a good tip that's the given that excuse me gives a good rating that's the given what is your probably respondent had lunch so we look over here in the service good rating this is a column number and we're looking at what is the probability that if the service rating was good that it was lunch so we look up here we want the column percent which is the second number and that is here sixty six point six seven or point six six seven if we get that to decimal and that is the answer there so we can answer the last part part C as well using this contingency table the question is are the events poor service and dinner independent well we can look at that two different ways and we're going to look at the answer here the way they're looking at it is the probability of poor given dinner equal to or not equal to poor so let's look over here in our table poor the probability of poor we look down in this column service pours at the bottom that's 58 out of 133 which is if we look at the percent of the total which is the last value in parentheses forty three point six one percent the probability of poor given dinner is this row remember because we've got given that's the clue that it's the the thing after the bar so we look at the row percent which is sixty one point five four because sixty one point five four is not equal to forty three point six one then they are not independent and so that's your answer here no because the probability of poor given dinner is not equal to the probability of poor hope this helps