# The concentration of active ingredient in a liquid laundry detergent

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.

(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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