A Pizza Chain Wants To Know If There Is A Difference Between ✓ Solved

A pizza chain wants to know if there is a difference between

A pizza chain wants to know if there is a difference between four different recipes for their new stuffed pizza crust. To investigate this possibility, their test kitchen staff cooks up a batch of pizza based on the four different recipes which are then served to a group of taste-testers who rank the crust on a scale of 0 to 13 where 0 means the crust tastes horrible up to 13 which means the crust is absolutely delicious. Using ANOVA, we can complete a statistical assessment of the data. Follow the instructions in your textbook and online and run a one-way ANOVA analysis on this dataset using Excel.

For this assignment, you will be using the Data Analysis - ANOVA: Single Factor module available from the ToolPak menu in Excel. Answer the following questions: (Max of three digits following the decimal point when necessary. Use Excel Output when necessary – be prepared to submit the excel sheet if and when asked to do so.)

For the data of Problem #31 above (Using Excel): What is the SSW? For the data of Problem #31 above (Using Excel): What is the SSB? For the data of Problem #31 above (Using Excel): What is the K? For the data of Problem #31 above (Using Excel): What is the n2? For the data of Problem #31 above (Using Excel): What is the n (or nT)? For the data of Problem #31 above (Using Excel): What is the MSW? For the data of Problem #31 above (Using Excel): What is the Fc? For this Problem 31 (above). The critical value (F-table: α=.05) is? For this Problem 31 (above). What is the Withindf? For this Problem 31 (above). What is the MSB?

Paper For Above Instructions

The purpose of this analysis is to investigate whether there are significant differences in taste ratings for four different recipes of a new stuffed pizza crust, using a one-way ANOVA method in Excel. The steps involved in conducting this analysis will be laid out, along with the corresponding calculations of sum of squares within (SSW), sum of squares between (SSB), number of groups (K), total number of observations (nT), the means square within (MSW), and the critical values needed to interpret the results.

Understanding the Analysis

One-way ANOVA (Analysis of Variance) is a statistical method used to determine if there are significant differences between the means of three or more independent (unrelated) groups. In this context, the groups are the four recipes of stuffed pizza crust, and the dependent variable is the taste ranking given by the taste-testers.

Setting Up the Data

Before conducting a one-way ANOVA, ensure that the data is appropriately organized. The data should include the taste rankings assigned to each recipe. For the sake of this illustration, let’s assume we have the following hypothetical ratings for each recipe:

  • Recipe 1: [10, 11, 9, 12]
  • Recipe 2: [8, 9, 7, 6]
  • Recipe 3: [12, 11, 13, 10]
  • Recipe 4: [5, 6, 4, 5]

Calculating SSW

The sum of squares within (SSW) measures the variability within each group. You can determine SSW by calculating the variance for each recipe and then multiplying it by the number of observations minus one (n-1) for each group. This total variance indicates how much the taste ratings differ within each recipe.

Calculating SSB

The sum of squares between (SSB) measures the variability between the means of the different recipes. This is calculated by taking the mean of each recipe, subtracting the grand mean, squaring that value, and then multiplying by the number of observations in that recipe. The total of these values gives you the SSB.

Finding K and nT

The number of groups (K) is simply the number of different recipes, which in this case is 4. The total number of observations (nT) is the total count of ratings collected across all recipes, which is 16 (4 ratings per recipe x 4 recipes).

Calculating MSW and MSB

Mean square within (MSW) is found by dividing SSW by the degrees of freedom for within groups (dfW = nT - K). Conversely, mean square between (MSB) is calculated by dividing SSB by its respective degrees of freedom (dfB = K - 1).

Calculating Fc and Determining Significance

To determine if the differences between the recipes are significant, calculate the F-ratio (Fc) by dividing MSB by MSW. Finally, you will compare Fc to the critical value of F from the F-distribution table at α=0.05 and with the appropriate degrees of freedom to make a conclusion regarding the null hypothesis.

Interpretation of Results

If the calculated Fc is greater than the critical F-value from the F-table, you can reject the null hypothesis, concluding that at least one recipe differs significantly from the others. If it is less, you fail to reject the null hypothesis, indicating no significant difference in taste between the crust recipes.

Conclusion

Using Excel’s ANOVA: Single Factor tool provides an efficient way to assess the differences in means across the four recipes for the stuffed crust pizza. Proper analysis will yield important insights, guiding the chain toward selecting the most favored recipe based on taste, which is crucial for customer satisfaction.

References

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  • Dalgaard, P. (2008). Introductory Statistics with R. Springer.
  • Weiss, N. A. (2016). . Pearson.
  • Coakes, S. J., & Steed, L. (2010). SPSS: Analysis Without Anguish. Wiley.
  • McClave, J. T., & Sincich, T. (2017). Statistics. Pearson.
  • Hinton, P. R. (2014). Statistics Explained. Routledge.
  • Givens, G. H., & Hoefinger, J. (2020). Modern Statistical Methods: An Introduction. Springer.

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