Posted: August 29th, 2021

The concentration of active ingredient in a liquid laundry detergent

 

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1. The concentration of active ingredient in a liquid laundry detergent is thoughtto be effected by the type of catalyst used in the process. The standard deviation of active concentration is known to be 3 grams per liter, regardless of the catalyst type. Ten observations on concentration are taken with each catalyst, and the data are shown here: Catalyst 1: 66.1, 64.0, 64.4, 60.0, 65.3, 66.9, 61.5, 63.5, 61.6, 62.3Catalyst 2: 66.3, 64.7, 67.6, 68.5, 68.3, 67.4, 66.1, 69.9, 70.6, 68.7

 

(a) Find a 95% confidence interval on the difference in mean active concentrations for the two catalysts.

 

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(b) Is there any evidence to indicate that the mean active concentrations depend on the choice of the catalyst? Base your answer on the results of part (a).

 

2. A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: ¯x1 = 9.85, s21 = 6.79 and n1 = 10. After installation, a random sample resulted in ¯x2 = 8.08, s22 = 6.18, and n2 = 8.

 

(a) Can you conclude that the two variances are equal? (use α = 0.05).

 

(b) Can you conclude that the new purification device has reduced the mean percentage of impurity? (use α = 0.05).

 

 

 

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