Part b for this part the snack machine has an alert...

Part B: For this part, the snack machine has an alert mechanism that notifies the vending machine company if a certain number (N) of unsuccessful vending errors happen. People are pushing the wrong numbers – either requesting lots of missing snacks (maybe the most popular snacks are missing) or straining the claw by requesting the locations the claw is using. A vend error is when the snack machine tries to vend from an empty snack slot, or if the vending input is in the same space as the claw (e.g., L=3, T=3).

Transcript

00:01 So we have a vending machine company that wants to check if three of its machines are properly dispensing 12 ounces of coffee.

00:06 So machines a, b, and c, here's the data.

00:10 And then the question, the actual question being asked is, is there a significant difference between the vending machines a, b, and c? so the question isn't, are the machines all dispensing 12 ounces? is it, are they all dispensing the same? or are they all different? or is there some difference? so our null hypothesis is that the mean of a is equal to the mean of b is equal to the mean of c.

00:28 The alternative is that the means are not equal.

00:31 And we're going to use this, test this at the alpha of 0 .05 level of significance, which means we're going to get a p value.

00:38 And if the p value is less than the alpha, we're going to reject our null hypothesis.

00:41 And we're going to use a one -way anova here, anova.

00:46 Again, the question was, is there a significant difference between the vending machines a, b, and c? and that's why we're going to use this anova here.

00:55 So we're going to fill in this table here and we need the p value, but to get the p value, we need the f statistic.

01:00 And the f statistic is found by taking the mean square of the between groups, msb, divided by the mean square of the within groups.

01:08 Great.

01:08 So we need the mean squares.

01:09 The mean squares are found by taking the sum of squares divided by their corresponding degrees of freedom.

01:14 We don't have any of those, but this is where our work is going to come into play.

01:17 So the degrees of freedom for the between groups is given as k minus one.

01:21 So k is the number of groups.

01:22 So k is equal to three.

01:25 Three minus one is going to be two.

01:29 Within, degrees of freedom is found by taking n minus k, where n is the total number of samples taken.

01:35 So there's three times 15.

01:36 So big n is 15.

01:39 15 minus three.

01:42 Then lastly, the total is the sum of those.

01:44 The total degrees of freedom is the sum here.

01:46 So it's 14.

01:49 Excellent.

01:50 Now we need the sum of squares.

01:52 So there's a relationship between the sum of squares.

01:54 The sum of squares of the total is equal to the sum of squares of the between plus the sum of squares of the within.

01:59 So we're going to find the total and the between and then take the difference to get the within.

02:03 Because if we just subtract the between from the total, you get the within.

02:08 Kind of a fun little relationship there.

02:10 So let's go ahead and work through the total first.

02:15 It says t is equal to the sum of each x value minus the grand mean x bar sub g squared.

02:22 Let's go ahead and get that.

02:27 And here we go.

02:29 So here's the average of all 15 values.

02:33 11 .96.

02:34 I just highlight the average function of the spreadsheet equals average.

02:42 And then you put in your cell data.

02:43 You could also just add them up, divide by 15.

02:45 That works too...

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