When a problem asks you to conduct a statistical test, do so formally. Think car
ID: 3364899 • Letter: W
Question
When a problem asks you to conduct a statistical test, do so formally. Think carefully about the appropriate test to use for the circumstances in the problem, state the null and alternative hypotheses, record the level of significance used, calculate the test statistic, compare it to the critical value of the statistic (tables on our Blackboard site), accept or reject the null hypothesis, and state your results. Show your work.
1. Mean sand grain size in “phi” units has been determined for 13 active (migrating) sand dunes and 11 neighboring stabilized sand dunes. Phi units represent an interval scale of measurement. Because the mean grain size for each dune was determined from laboratory analysis of only one baggy full of sand randomly sampled from each dune, there is not a great deal of confidence in these data despite their being independent observations and interval-scale data. Nothing is known of the frequency distribution(s) of the population(s) from which the samples were drawn.
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Active Dunes Active Phi Mean Dune # Gr. Size Stabilized Dunes Stable Dune # Phi Mean Gr. Size 2.96 3.09 3.11 2.70 2.96 2.72 2.69 2.72 2.54 2.51 2.55 2.52 2 60 3.01 2.84 3.03 2.93 2.91 2.86 2.87 3.31 3.22 3.24 3.27 4 4 10 10 12Explanation / Answer
Result:
When a problem asks you to conduct a statistical test, do so formally. Think carefully about the appropriate test to use for the circumstances in the problem, state the null and alternative hypotheses, record the level of significance used, calculate the test statistic, compare it to the critical value of the statistic (tables on our Blackboard site), accept or reject the null hypothesis, and state your results. Show your work.
No.
Label
Data
Rank
1
active
2.96
15.5
2
active
3.09
19
3
active
3.11
20
4
active
2.7
7
5
active
2.96
15.5
6
active
2.72
8.5
7
active
2.69
6
8
active
2.72
8.5
9
active
2.54
3
10
active
2.51
1
11
active
2.55
4
12
active
2.52
2
13
active
2.6
5
14
stable
3.01
17
15
stable
2.84
10
16
stable
3.03
18
17
stable
2.93
14
18
stable
2.91
13
19
stable
2.86
11
20
stable
2.87
12
21
stable
3.31
24
22
stable
3.22
21
23
stable
3.24
22
24
stable
3.27
23
Wilcoxon - Mann/Whitney Test
n
sum of ranks
13
115
active
11
185
stable
24
300
total
U =13*11+13*14/2-115 =119
Z =(119-13*11/2) /sqrt(13*11*25/12)
=2.751
Calculated z= 2.751 > 2.33 the critical value at 0.01 level. ( one tailed test).
Ho is rejected.
We conclude that stabilized dune have a larger phi mean grain size than active dunes.
No.
Label
Data
Rank
1
active
2.96
15.5
2
active
3.09
19
3
active
3.11
20
4
active
2.7
7
5
active
2.96
15.5
6
active
2.72
8.5
7
active
2.69
6
8
active
2.72
8.5
9
active
2.54
3
10
active
2.51
1
11
active
2.55
4
12
active
2.52
2
13
active
2.6
5
14
stable
3.01
17
15
stable
2.84
10
16
stable
3.03
18
17
stable
2.93
14
18
stable
2.91
13
19
stable
2.86
11
20
stable
2.87
12
21
stable
3.31
24
22
stable
3.22
21
23
stable
3.24
22
24
stable
3.27
23
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