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The concentration of active ingredients in a liquid laundry detergent is thought to be affected 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, 62.3
Catalyst 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 for the difference in mean concentration between the two catalysts.

Answer :

Final Answer:

The given data presents the active ingredient concentrations for two different catalysts used in a liquid laundry detergent manufacturing process. To determine if there's a significant difference in mean concentration between Catalyst 1 and Catalyst 2, a 95% confidence interval for the mean difference must be established. By analyzing the provided concentration data and employing statistical methods, we can ascertain this confidence interval.

Explanation:

To compute the confidence interval, we first calculate the mean concentration for each catalyst. For Catalyst 1, the mean is 63.56 grams per liter, and for Catalyst 2, it's 67.21 grams per liter. The difference in means is 3.65 grams per liter. Afterward, we compute the standard error of the difference, which is 0.9487 grams per liter.

Utilizing the t-distribution with 9 degrees of freedom and a 95% confidence level, the critical value is approximately 2.262. The margin of error is then calculated by multiplying the standard error by the critical value, yielding 2.1476 grams per liter. Finally, the confidence interval is determined by subtracting and adding the margin of error to the difference in means, resulting in a 95% confidence interval of -0.753 to 7.603 grams per liter. Therefore, the correct option is (d).

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