Question

1. An “identical” experiment has been completed by 14 different laboratories. The laboratories were of a wide quality - some were excellent; some less so. This experiment involved producing a certain solution which would react when exposed to ultraviolet radiation. The reaction was expected to be inhibited by addition of a certain chemical agent. The average reaction rate was determined and reported by each group. The results are in table 1. a) Provide the degrees of freedom and the table value. b) Determine the means for the experiment with and without the chemical agent. Provide a plot of the average reaction rate as a function of the case. Show error bars that indicate the statistical uncertainty for 95% confidence. Can you say that the chemical agent inhibited the reaction? Why or why not? (Hints: + Error = ttable x SSD) c) Using Minitab, determine the p-value. Determine if the null hypothesis may or may not be rejected. State the conclusion of this test. d) Using Minitab, complete a t-test for paired samples. Provide the tdata value and p-value. Determine if the null hypothesis may or may not be rejected. State the conclusion of this test. e) Discuss the above results. In particular, explain why the results in parts "c" and "d" are different. Which would you recommend as more relevant? Why?

Answer 1

(a) df = 14 - 1 = 13

t-table value = 2.160

(b)

0.047429	mean With Agent
0.038429	mean Without Agent
0.009000	mean difference (With Agent - Without Agent)

Boxplot of Differences (with Ho and 95% t-confidence interval for the mean) Но -0.01 0.00 0.01 0.03 0.04 0.02 Differences

(c) The p-value is 0.0453.

(d) Since the p-value (0.0453) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the chemical agent inhibited the reaction.

(e) The results are the same.

With Agent	Without Agent
0.026	0.026
0.052	0.047
0.045	0.005
0.09	0.088
0.012	0.02
0.084	0.087
0.006	0.007
0.078	0.074
0.016	0.015
0.005	0.001
0.12	0.08
0.055	0.035
0.055	0.035
0.02	0.018

0.047429	mean With Agent
0.038429	mean Without Agent
0.009000	mean difference (With Agent - Without Agent)
0.015206	std. dev.
0.004064	std. error
14	n
13	df
2.215	t
.0453	p-value (two-tailed)