Question

(1) A researcher has collected mass data for seven fish collected from each of six small ponds in central California. The researcher is interested in whether any of the ponds seem to have larger or smaller fish than the others. The data is: Bell 23 26 29 Marston 24 26 23 18 23 25 Fish # Adler Linde Morgan 18 Pearson 20 20 17 20 24 28 20 21 20 28 20 23 21 26 25 26 23 29 21 25 (a, 2 pts) What is Fmax for your preliminary variance equality F test? (round to nearest 0.001) Critical Fmax (b, 2 pts) What is the critical Fmax value for this F test? (Use the Fmax table posted on the website and a 0.05) (c, 1 pt ea) Complete the ANOVA table below. Provide a range for the p value using the tables provided on the course website. (round all non-integer values to nearest 0.001 Source df Among Within Total MS (d, 3 pts) What is your conclusion? Use the grammar described in lecture and state with what degree of confidence you make your conclusion by providing the most specific range of p values from the table provided in lecture. You must use the phrase "significantly different" or "not significantly different" in your answer. Also, if any means appear to be different, make your best guess as to the most likely pair that differ. Note: no credit will be given for ANY text outside the box or hard to read answers

Answer 1

Solution:

Here we have data:

Fish	Adler	Bell	Linde	Marston	Morgan	Pearson
1	18	23	18	24	18	20
2	20	26	21	26	15	19
3	17	29	22	23	19	20
4	20	22	26	18	23	28
5	24	29	25	23	21	20
6	28	21	26	25	18	19
7	20	25	23	22	19	21

Here we are using Excel for calculation:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	7	147	21	14.333
Column 2	7	175	25	10.333
Column 3	7	161	23	8.667
Column 4	7	161	23	6.667
Column 5	7	133	19	6.333
Column 6	7	147	21	10
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	154	5	30.8	3.280	0.015	2.477
Within Groups	338	36	9.389
Total	492	41

Hypothesis:

H_o; μ1 = μ2 = μ3 = μ4 = μ5 = μ6

H_a; At least one mean is different from others.

Test statistics:

F_max = 3.280

Critical Value:

F_max = 2.477

Reject the null hypotheses.

Here we have sufficient evidence to reject the null hypothesis , Test statistics (3.280) is grater than critical value (2.477).