# Statistics: Analyzing Data

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Questions:

1. For day 1 only (30 samples total), what is the density average and standard deviation?

2. For all days and all samples, what is the density average and standard deviation? Remember, these are samples of density, not the entire population.

3. For Day 1 only (30 samples), is the pavement density greater than 91.0% with 95% confidence?

4. For all days and all samples, is the pavement density greater than 91.0% with 95% confidence?

5. What are your answers for #3 and #4 if the density value is 91.5%?

6. What are your answers for #3 and #4 if the density value is 92.0%?

Does what you calculate make sense to you?

Hot mix asphalt pavement density measurements on a 15,987 ton job
Lot Number Lot_Date
1
Day 1
2
Day 1
3
Day 1
4
Day 1
5
Day 1
6
Day 1
7
Day 2
8
Day 2
9
Day 2
10
Day 2
11
Day 3
12
Day 3
13
Day 3
14
Day 4
15
Day 4
16
Day 4
17
Day 4
18
Day 5
19
Day 5
20
Day 5
21
Day 5
22
Day 6
23
Day 6
24
Day 6
25
Day 6
26
Day 6
27
Day 7
28
Day 7
29
Day 7
30
Day 7
31
Day 8
32
Day 8
33
Day 8
34
Day 8
35
Day 8
36
Day 8
37
Day 9
38
Day 9
39
Day 9
40
Day 9
Lot Size
(tons)
433
400
400
400
400
315
400
400
448
450
400
400
443
400
400
400
257
400
400
400
160
400
400
400
400
413
400
400
400
125
400
400
400
400
400
305
400
400
400
400
Measured Density (% Rice)
Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
96.2
91.2
96.2
96.8
94.8
91.0
91.2
91.1
91.3
94.9
92.5
91.2
93.1
91.7
92.0
91.1
94.2
91.5
91.7
92.8
92.3
91.8
92.2
91.7
92.7
92.2
91.1
93.0
93.2
91.9
91.3
91.4
92.2
90.9
91.6
93.1
92.3
92.0
91.0
90.9
90.8
91.2
91.5
91.3
90.9
91.1
91.5
90.8
92.6
91.4
91.5
91.4
91.1
91.0
90.9
92.8
92.2
93.8
91.7
92.6
92.7
93.3
91.8
91.7
91.3
93.4
91.4
93.8
93.6
93.5
92.5
94.9
92.0
91.0
93.1
92.1
92.3
92.7
92.6
91.1
91.1
91.8
91.6
91.7
92.0
93.3
93.6
93.1
91.8
92.4
91.5
91.0
92.4
91.7
91.8
92.2
93.3
91.5
90.8
92.7
92.2
91.9
91.5
92.0
91.9
91.6
91.2
91.7
91.9
91.7
91.0
91.0
92.1
92.2
91.5
91.5
91.0
91.6
91.8
91.3
91.5
91.7
91.0
91.2
91.7
92.7
91.2
92.3
91.0
91.7
91.5
92.6
91.2
93.6
91.9
91.7
95.8
91.6
91.6
91.3
92.6
91.9
91.8
93.3
93.5
92.7
92.4
93.4
91.6
91.1
92.6
92.6
91.5
92.1
91.4
91.8
92.5
93.9
93.0
91.6
92.3
92.6
91.6
92.3
91.4
92.6
91.0
92.8
91.7
91.7
92.4
91.6
92.9
92.5
91.8
92.6
92.6
91.0
93.4
91.5
92.6
91.1
94.5
91.6
91.4
91.1
91.7
91.6
92.6
91.9
91.3
91.1
92.5
91.9
91.0
91.2
91.0
91.0
91.0
91.2
These densities are t
less. Either way, it m
here.
Densities are measu
possible density (if th
Density). Therefore,
the mixture being m
As you can see the d
project the specified
to 92.0%).
41
42
43
Day 9
Day 10
Day 10
85
400
153
15987
91.3
91.7
92.3
91.9
92.0
92.0
90.7
94.1
90.7
91.3
91.8
90.5
90.9
92.9
90.2
These densities are taken 5 for every 400 tons paved (more or less). There
are allowances made for the end of a day to have that amount be more or
less. Either way, it makes no difference for what you are being asked to do
here.
Densities are measured and expressed as a percentage of the maximum
possible density (if there were no air voids in the mixture, called Rice
Density). Therefore, a density of 91.8% means that there are 8.2% air voids in
the mixture being measured.
As you can see the densities measured vary each day. At the time of this
project the specified minimum density was 91.0% (FYI: it has now been raised
to 92.0%).

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