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components that are out of specification among the three methods. After conducting the analysis, report the findings to the management team. Due to a recent change by Microsoft, you will need to open the XLMiner Analysis ToolPak add-in manually from the home ribbon. Screenshot of ToolPak Open spreadsheet a. Compute the sum of squares between treatments (assembly methods). b. Compute the mean square between treatments (to 1 decimal if necessary). c. Compute the sum of squares due to error. d. Compute the mean square due to error (to 1 decimal if necessary). f. At the α = 0.01 level of significance, test whether the means for the three methods are equal. Calculate the value of the test statistic (to 2 decimals). The p-value is (to 4 decimals): A manufacturing company has been selected to assemble a small but important component that will be used during the construction of numerous infrastructure projects. The company anticipates the need to assemble several million units over the next several years. Company engineers elect three potential assembly methods: Method A, Method B, and Method C. Management would like to select the method that produces the fewest number of parts per 10,000 parts produced that do not meet specifications. It may also be possible that there is no statistical difference between the three methods, in which case the lowest cost method will be selected for production. While all parts are checked before leaving the factory, the best method will reduce the number of parts that need to be recycled back into the production process. To test each method, six batches of 10,000 components are produced using each of the three methods. The number of components out of specification are recorded in the Microsoft Excel Online file below. Analyze the data to determine if there is any difference in the mean number of components that are out of specification among the three methods. After conducting the analysis, report the findings to the management team. Due to a recent change by Microsoft, you will need to open the XLMiner Analysis ToolPak add-in manually from the home ribbon. Screenshot of ToolPak. Open spreadsheet. a. Compute the mean square between treatments (to 1 decimal if necessary). ANOVA Completely Randomized Design Method A Method B 163 146 142 157 168 125 145 146 149 137 6 187 147 c. Compute the sum of squares due to error. Batch Method C 123 122 133 144 154 128 d. Compute the necessary? Set up the ANOVA table for this problem. Round all sum of squares to the nearest whole number. Round all Mean Squares to Source of Variation Sum of Squares Degrees of Freedom Mean Square Treatments (Methods) Error Total f. At the α = 0.01 level of significance, test whether the means for the three methods are equal. Calculate the value of the test statistic (to 2 decimals). The p-value is (to 4 decimals):

Name: components that are out of specification among the three methods after conducting the analysis report the findings to the management team due to a recent change by microsoft you will need to 94856
Uploaded: 2023-09-03T20:40:14-08:00
Duration: 7 min 17 s
Channel: Jon Southam
Description: components that are out of specification among the three methods after conducting the analysis report the findings to the management team due to a recent change by microsoft you will need to 94856

components that are out of specification among the three methods. After conducting the analysis, report the findings to the management team.

Due to a recent change by Microsoft, you will need to open the XLMiner Analysis ToolPak add-in manually from the home ribbon. Screenshot of ToolPak
Open spreadsheet
a. Compute the sum of squares between treatments (assembly methods).
b. Compute the mean square between treatments (to 1 decimal if necessary).
c. Compute the sum of squares due to error.
d. Compute the mean square due to error (to 1 decimal if necessary).
f. At the α = 0.01 level of significance, test whether the means for the three methods are equal.
Calculate the value of the test statistic (to 2 decimals).
The p-value is (to 4 decimals):

A manufacturing company has been selected to assemble a small but important component that will be used during the construction of numerous infrastructure projects. The company anticipates the need to assemble several million units over the next several years. Company engineers elect three potential assembly methods: Method A, Method B, and Method C. Management would like to select the method that produces the fewest number of parts per 10,000 parts produced that do not meet specifications. It may also be possible that there is no statistical difference between the three methods, in which case the lowest cost method will be selected for production. While all parts are checked before leaving the factory, the best method will reduce the number of parts that need to be recycled back into the production process.

To test each method, six batches of 10,000 components are produced using each of the three methods. The number of components out of specification are recorded in the Microsoft Excel Online file below. Analyze the data to determine if there is any difference in the mean number of components that are out of specification among the three methods. After conducting the analysis, report the findings to the management team.

Due to a recent change by Microsoft, you will need to open the XLMiner Analysis ToolPak add-in manually from the home ribbon. Screenshot of ToolPak. Open spreadsheet.

a. Compute the mean square between treatments (to 1 decimal if necessary).
ANOVA Completely Randomized Design Method A Method B 163 146 142 157 168 125 145 146 149 137 6 187 147
c. Compute the sum of squares due to error.
Batch
Method C 123 122 133 144 154 128
d. Compute the necessary? Set up the ANOVA table for this problem. Round all sum of squares to the nearest whole number. Round all Mean Squares to
Source of Variation Sum of Squares Degrees of Freedom Mean Square Treatments (Methods) Error Total
f. At the α = 0.01 level of significance, test whether the means for the three methods are equal.
Calculate the value of the test statistic (to 2 decimals).

The p-value is (to 4 decimals):

components that are out of specification among the three methods after conducting the analysis report the findings to the management team due to a recent change by microsoft you will need to 94856

Added by Carlos A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jon Southam

09/03/2023

Step 1

- Calculate the overall mean: (163 + 146 + 142 + 157 + 168 + 125 + 145 + 146 + 149 + 137 + 6 + 187 + 147 + 123 + 122 + 133 + 144 + 154 + 128) / 18 = 141.67 - Calculate the sum of squares between treatments: SS_between = (6*(163-141.67)^2) + (6*(146-141.67)^2) + Show more…

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components that are out of specification among the three methods. After conducting the analysis, report the findings to the management team. Due to a recent change by Microsoft, you will need to open the XLMiner Analysis ToolPak add-in manually from the home ribbon. Screenshot of ToolPak Open spreadsheet a. Compute the sum of squares between treatments (assembly methods). b. Compute the mean square between treatments (to 1 decimal if necessary). c. Compute the sum of squares due to error. d. Compute the mean square due to error (to 1 decimal if necessary). f. At the α = 0.01 level of significance, test whether the means for the three methods are equal. Calculate the value of the test statistic (to 2 decimals). The p-value is (to 4 decimals): A manufacturing company has been selected to assemble a small but important component that will be used during the construction of numerous infrastructure projects. The company anticipates the need to assemble several million units over the next several years. Company engineers elect three potential assembly methods: Method A, Method B, and Method C. Management would like to select the method that produces the fewest number of parts per 10,000 parts produced that do not meet specifications. It may also be possible that there is no statistical difference between the three methods, in which case the lowest cost method will be selected for production. While all parts are checked before leaving the factory, the best method will reduce the number of parts that need to be recycled back into the production process. To test each method, six batches of 10,000 components are produced using each of the three methods. The number of components out of specification are recorded in the Microsoft Excel Online file below. Analyze the data to determine if there is any difference in the mean number of components that are out of specification among the three methods. After conducting the analysis, report the findings to the management team. Due to a recent change by Microsoft, you will need to open the XLMiner Analysis ToolPak add-in manually from the home ribbon. Screenshot of ToolPak. Open spreadsheet. a. Compute the mean square between treatments (to 1 decimal if necessary). ANOVA Completely Randomized Design Method A Method B 163 146 142 157 168 125 145 146 149 137 6 187 147 c. Compute the sum of squares due to error. Batch Method C 123 122 133 144 154 128 d. Compute the necessary? Set up the ANOVA table for this problem. Round all sum of squares to the nearest whole number. Round all Mean Squares to Source of Variation Sum of Squares Degrees of Freedom Mean Square Treatments (Methods) Error Total f. At the α = 0.01 level of significance, test whether the means for the three methods are equal. Calculate the value of the test statistic (to 2 decimals). The p-value is (to 4 decimals):

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Transcript

00:01 All right, so we're looking at some data here.

00:02 There are three methods of production, a, b, and c.

00:05 And what we're looking at within each of the three methods are six batches of 10 ,000 components.

00:13 And these are the faulty parts that are constructed, or that are produced within those batches.

00:20 And so we want to know if there's a significant difference between the methods.

00:26 So our null hypothesis will be that the means are all equal.

00:30 Mu one is equal to mu two is equal to mu three.

00:32 And i wrote a one instead of a two, sorry about that.

00:37 The alternative hypothesis is that the means are not all equal.

00:48 All right, and so we're gonna run a one -way anova on this.

00:52 And so we have the, i went ahead and calculated the sample sizes of each, so six, the sums, you add all of them up.

01:00 The means, you take the sums of the sample size.

01:03 And 159, 142, 134, those are the sample means.

01:06 And we want to see are they all equal.

01:10 And we have the variances here.

01:12 And the variance, i use the var .s function and put in your data, and then that's in the spreadsheet.

01:20 And those are the variances, square root of that, number is the same deviations.

01:24 So we can see those statistics here based on those samples.

01:29 And the grand mean is 145.

01:33 You take the grand mean of all the data here.

01:36 There are three groups, k is three.

01:38 Big n, the total observation count is 18, six times three.

01:44 We're gonna use this information to fill in our anova table.

01:48 And we should say that we're gonna test this significant, this hypothesis at the alpha 0 .01 level of significance, which means if our p -value falls less than this alpha, we're gonna reject the hypothesis.

02:01 So to fill in this table, we want the p -value.

02:05 To get the p -value, we need the f statistic.

02:07 That's the mean square of the treatments divided by the tr, divided by the mean square of the error.

02:15 The mean squares of the treatment and the error are found by taking their corresponding sum of squares divided by the degrees of freedom.

02:21 So this is where our calculations lie.

02:24 Degrees of freedom treatment, degrees of freedom is k minus one, k is three, so this is gonna be two.

02:38 And the error, the degrees of freedom is n minus k, so 18 minus three is gonna be 15.

02:45 And then the total degrees of freedom is big n minus one, so 17.

02:51 Just gotta clean up our workspace here.

02:55 Great, now we need our sum of squares...

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