Suppose that you were interested in studying the effect of...

Suppose that you were interested in studying the effect of temperature on the yield of a chemical process, and that 3 batches were produced at each of three temperatures, producing the following table of data: (with 45°C = Treatment 1; 55°C = Treatment 2; and 65°C = Treatment 3) 45°C 55°C 65°C 35 22 30 37 26 29 31 23 31 Use the Excel-generated Single-Factor ANOVA results to calculate the Left-Hand Endpoint (LHEP) of the 90% Fisher's LSD Confidence Interval (CI) estimate. Round off your answer to the fourth decimal place. Anova: Single Factor SUMMARY Groups Count Sum Average Variance 45°C 3 103 34.33333333 9.333333333 55°C 3 71 23.66666667 4.333333333 65°C 3 90 30 1 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 172.6666667 2 86.33333333 17.6591 0.0031 5.143 Within Groups 29.33333333 6 4.888888889 Total 202 8 The LHEP requested above and rounded off as instructed is: Blank 1.

Transcript

00:01 Once again, welcome to a new problem.

00:04 This time we're dealing with inferential statistics.

00:08 We're dealing with inferential statistics.

00:12 And under inferential statistics, we have hypothesis testing.

00:19 We have hypothesis testing and we also have estimation.

00:26 We have estimation.

00:27 We have estimation.

00:28 We always see estimation as confidence.

00:31 Intervals and when it comes to hypothesis testing we have numerical options rather numerical variables that we deal with under hypothesis testing and we also have categorical variables and when it comes to numerical variables we could have a dependent samples t -test and we could also have an independent samples t test.

01:10 An extension of the independent samples t test happens to be the anova which so for the independent samples t test you're mostly dealing with two groups for the anova you're dealing with two or more groups and for the anova this is the analysis this is analysis of variance.

01:38 So we have the analysis of variance under the anova.

01:42 And the f ratio is the test statistic for the analysis of variance where we have the mean square between groups over the main square within groups and the between groups mean square is sum of squares between groups over degrees of freedom between groups and some of squares within groups over degrees of freedom within groups.

02:11 So assume we have a table and our goal is to determine, determine the impact of temperature on the yield of a chemical process, of a chemical process and we do have three batches at different temperatures.

02:53 So we have three batches at different temperatures.

02:55 So we have three batches at different temperatures.

02:58 The first one is 45 degrees celsius.

03:03 That's the first treatment.

03:06 And then the second treatment is the second treatment.

03:12 Happens to be at 55 degrees celsius and third treatment happens to be at 65 degrees celsius so in terms of the yield at these different temperatures these are the numbers that we do have these are the numbers that we do have so the question here is using using single factor using single factor an over compute the left hand point with the left hand point and that's the lhdp the left hand endpoint sorry this is endpoint off the 90 percent uh fishers lsd, confidence, confidence interval, estimate for these numbers.

04:41 So the first thing we're going to do is we'll build up on an over table, another single factor, summary.

04:58 So we have groups, we have three groups.

05:00 There are 45 celsius, 55 celsius, and 65 celsius.

05:11 And then we have the count three, three, three.

05:22 We have one or three.

05:38 We have average variance.

05:51 And then at 90, we have 31.

05:55 So these are your results, including.

05:58 The degrees of freedom that you deal with...