The concentration of active ingredient in a liquid laundry d

The concentration of active ingredient 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. The distribution is also known to be normal. Ten observations on concentration are taken with each catalyst, and the data follow: Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0 Catalyst 2: 66.4, 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8 (For this question, to decide on the test statistic only check whether the population variances are known or not. Neglect sample sizes.) Find a 95% confidence interval on the difference in mean active concentrations for the two catalysts. Is there any evidence to indicate that the mean active concentrations depend on the choice of catalyst? Base your answer on the results of part (a).

Solution

  t = 2.4681
  df = 18
  standard error of difference = 1.297

The two-tailed P value equals 0.0238
   this difference is considered to be statistically significant.

The mean of Catalyst 1 minus Catalyst 2 equals -3.200
  95% confidence interval of this difference: From -5.924 to -0.476

b) Yes there is evidence to indicate the mean active concentr. depend on the choice of catalyst as confidence interval does not contain 0 in it at 95%

Also p value <0.05

Group	Catalyst 1	Catalyst 2
Mean	65.220	68.420
SD	3.444	2.224
SEM	1.089	0.703
N	10	10