# Hypothesis Testing:ANOVA and Variance

#1

In a drug firm, the variation in the weight of an antibiotic from batch to batch is important.

With our present process, the standard deviation is 0.11 g. The research department has

developed a new process that it believes will produce less variation. The following weight

measurements (in grams) were obtained with the new process:

7.47

7.49

7.64

7.59

7.55

Does the new process have less variation than the old? Why?

#2

A manufacturer of rubber products is trying to decide which "recipe" to use for a particular rubber compound. High tensile strength is desirable. Recipe 1 is cheaper to mix, but he is not sure if its strength is about the same as that of recipe 2. Five batches of rubber were made by each recipe and tested for tensile strength. These are the data collected (in psi):

Recipe 1 Recipe2

3067 3200

2730 2777

2840 2623

2913 2044

2789 2834

Which recipe would you recommend? Why?

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#### Solution Preview

Please see the attachments.

Workings are given in the excel sheet.

#1

In a drug firm, the variation in the weight of an antibiotic from batch to batch is important.

With our present process, the standard deviation is 0.11 g. The research department has

developed a new process that it believes will produce less variation. The following weight

measurements (in grams) were obtained with the new process:

7.47

7.49

7.64

7.59

7.55

Does the new process have less variation than the old? Why?

Answer

The null hypothesis under consideration is

H0: The variation in new process ≥ 0.11( ≥ 0.11)

The alternative hypothesis is

H1: The variation in new process < 0.11( < 0.11)

The test statistic used is

Rejection Criteria: ...

#### Solution Summary

The solution provides step by step method for the calculation of Chi-square test statistic for testing variance and ANOVA. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.