Question

Clove oil and Tricaine mesylate (MS-222) are both used to anesthetize fish. Given a population of Fathead Minnows (Pimephales promelas), use the data to test the following claims.

         (a) Assuming the parent populations are essentially normal, test the claim that 80mg/L of MS-222 works faster than 80mg/L of Clove oil.

         (b) Assuming the parent populations are unknown, test the same claim in (a).

         (c) Using dose as the row variable and substance as the column variable, conduct a Two-way ANOVA and explain all results. Also explain why we actually should not use a Two-way ANOVA for this data.

Data: The following table shows the time to equilibrium loss (in minutes/seconds) for Fathead Minnows with different doses of Clove oil and MS-222. Note: Convert data to seconds.

Clove	Oil	MS -	222
60 mg/L	80 mg/L	60 mg/L	80 mg/L
0:28	0:48	2:00	2:30
2:42	0:40	1:00	1:25
1:45	0:46	2:42	1:44
2:45	2:30	0:43	0:53
0:36	4:45	1:00	0:55
1:12	6:27	2:00	0:58
2:03	3:29	1:37	1:13
0:56	1:08	6:21	5:43

Answer 1

(a) Assuming the parent populations are essentially normal,
test the claim that 80mg/L of MS-222 works faster than 80mg/L of Clove oil.

#Codes:
Convert the data into seconds as given below and then import the data into R.

Here Ho :Time taken by Clove Oil 80mg/L is greater than MS-222 80mg/L
t.test(dat$`Clove Oil 80 mg/L`,dat$`MS-222 80 mg/L`,"greater")

Output:

Welch Two Sample t-test

t = 0.67951, p-value = 0.2544

Since,p value is greater than 0.1,then Ho is accepted at 10% level of significance.

Data Set:

Clove Oil 60 mg/L	Clove Oil 80 mg/L	MS -222 60 mg/L	MS-222 80 mg/L
28	48	120	150
162	40	60	85
105	46	162	104
165	150	43	53
36	285	60	55
72	387	120	58
123	209	97	73
56	68	381	343