Four catalysts that may affect the concentration of one...

Four catalysts that may affect the concentration of one component in a three-component liquid mixture are being investigated. The following concentrations are obtained: 1 2 3 4 57.2 55.3 49.1 51.9 56.2 53.5 53.2 48.9 57.4 56.0 54.4 49.0 54.8 54.3 50.7 53.9 Provide analytical solutions to the following questions: a) Do the four catalysts have the same effect on the concentration? b) Formulate an appropriate statistical model and estimate the parameters. c) Construct, using all available information, a 95% confidence interval for the mean response for Catalyst 1.

Transcript

00:01 So for part a, effectively what we want to do is a hypothesis test, where the null hypothesis is going to be that the mean value for each one of the catalysts are all equal to each other.

00:16 The alternate hypothesis is that at least one, at least one mean value differs.

00:29 The appropriate way of doing this would be to use one factor.

00:36 Anova.

00:42 So what i'll do is show how to do this using excel.

00:46 So i'll bring this up.

00:48 I want to first copy in all of our data as well as put labels.

00:56 So actually, say, catalyst 1 and catalyst 2 and so on.

01:03 And if you drag this across, it should automatically fill in.

01:06 So we have 57 .2, 56 .2, 57 .4, 54 .8, and 53.

01:13 2 .9, 53, 53 .5, 56, 54 .3.

01:20 And we have 49 .1, 53 .2, 54 .4.

01:25 And lastly, we have 51 .9, 48 .9, 49 .0, and 50 .7.

01:30 So, having copied all the data in, we want to go to data analysis, anova, single factor.

01:38 Hit okay.

01:39 Put in our data, and note that we do have the data grouped by columns.

01:45 We have late.

01:45 In the first row.

01:48 Okay.

01:49 And so we can find that our f score here, 10 .0704, significantly greater than the critical value at this level of significance.

02:00 So we can conclude that it does appear that there is a significant, or that, pardon me, i'll say it this way.

02:09 Based on that result, so since we have that p equals 0 .00, oh is it? 0 .00.

02:17 135, 0135, we can reject the null hypothesis, concluding that at least one of the means differs.

02:30 For part b, in terms of the statistical model that's being referenced, and the parameters, what i'm guessing is that we want the mean value and the standard deviation for each one of those catalysts.

02:45 So what i'll do for that is i'll just do this in in excel here...

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