Transcript Northwest Ductless Heat Pump Pilot Project RTF Savings

DHP UES Key Issues & Decisions
Ecotope, Inc.
May 21, 2013
1 NORTHWEST ENERGY EFFICIENCY ALLIANCE
Agenda
Introduction
 Presentation Objectives
 Measure Description
 Research Structure
 Summary of Savings
 Summary of Key Issues
Issues & Strategies
Q&A
Motions
2
Introduction
3
Presentation Objectives
 Review research and findings for DHP pilot
evaluation (2008-2013)
 Develop a common foundation of understanding
for assessing DHP UES
 DHP performance
 Technical vs. behavioral and/or program design
considerations
 Key issues for DHP UES
 Make several fundamental decisions in advance
of full UES workbook presentation
4
Measure Description
Measure Classification
and Properties
Market Sector
Residential
Market Segment
Single-family
Measure Category
Seeking to convert provisional to
proven.
Measure Description
Install a ductless heat pump in
the main living area of an existing
zonal-electrically heated house.
5
DHP Research Structure
UES Workbook
Billing Analysis
~4,000 Participants
Market Progress
Evaluation
~300 Participants
Field Monitoring
95 Participants
Lab Testing
2 units
6
Saving Distribution, 3,887 kWh/yr
Electric Savings
Supplemental
Fuels
Takeback
7
Wide Range of DHP Savings

Metered sample

Billing Analysis
 Careful screening to ensure all-electric heat
 Measured heat contribution from the output of the DHP
 Analyzed pre-installation bills to establish base heating
use
 Screened based on poor VBDD fit
 Screened based on intake questionnaire
 Determined supplemental fuel savings impact
 Determined takeback from improved heating signature
 Lower R2 for pre-installation indicates an electric heat “takeback”,
 R2 measure fit, improves with more electric heat and with consistent
thermostat settings
 When pre-installation is lower screen and supplemental fuels flag is set to
zero, the screen is set assuming that this would indicate electric heat
takeback
 Substantial agreement with results of metered sample
8
Savings Vary by Screening Approach
Savings by Participant
Group
Screened bills: R2>.45,
Space Heat>0
Savings (kWh/yr)
Mean
EB
n
All
No Supplemental Fuels
Used
2081
81
3390
2719
90
2295
No Takeback (R2)
2976
101
1705
Metered Results: Measured Savings from Metered Sub-Sample
Total Savings (COP)
3887
375
65
Billing Analysis
3049
251
93
9
Electric
Savings
Supplemental
Fuels
Takeback
Summary of Issues
Issue 1: Which savings estimation approach:
Calibrated Engineering (SEEM) or
Statistical/Metastatistical (Billing & Metering)?
Issue 2: How to determine electric kWh savings
and supplemental fuel benefit?
Issue 3. How/whether to include “comfort” in
the measure savings and/or TRC calculation?
Issue 4. Should we combine the savings, or
disaggregate by climate zone?
10
Issue 1: Which savings estimation approach: Calibrated
Engineering (SEEM) or Statistical/Metastatistical (Billing &
Metering)?
11
UES Estimation Procedures
 Statistical




DHP pilot population only represents the pilot project participants and is not a representative
sample of the region
Pilot evaluation uses a large billing analysis with an intake questionnaire to provide participant
information
The billing analysis provides an impact evaluation framework but is not suited to developing the
determinants of consumption
More detailed information available on the performance of the DHP from lab and field monitoring
 Meta-Statistical



Both the billing analysis and the engineering analysis provide a direct measure of the savings
potential
Comparable studies in size and scope have not been attempted elsewhere
Small engineering studies in this region can be used to expand this analysis but are not focused on
this measure and the electric zonal heat population targeted
 Calibrated Engineering

Integrated research design focused on the performance characteristics of the DHP





12
Detailed lab testing of system performance
Submetering provide confirmation of lab test and determinants of consumption across a number of climates and
participants (95)
Testing and metering results allow the development of a DHP model within the SEEM simulation
Analysis shows the structure of the DHP performance in real homes
Calibration of SEEM model can be quite accurate and allow the results of the research to be
generalized for climates and house types
Tiered Research Approach Shows Agreement Among
Various Performance Measurements
Primary Measurements:
Calibrated Models:
Billing Data
Field measurements
& billing data agree
Field Energy Use
Measurements
Annual Energy Use
Simulation:
Final Savings Estimates
Billing & field data
used to calibrate
simulation
Field Performance
Measurements
Lab supports
field findings
Lab Measurements
13
DHP Performance
Simulation
Lab & field data
combine to develop
equipment
performance models
Measured Performance
Lab data forms the truth set for
performance measurements
 Provides critical insight into
equipment operation including





Maximum & minimum capacity
Low power cut off / cycling limit
Defrost operation
Indoor unit fan power
System standby power
Lab data verifies the accuracy
of the field measurements
Lab & field data combined to
develop equipment
performance models
14
Performance Curve Development

3 curves constructed from field data
 HSPF Levels: 12, 10.6, 8.2
 Curves are the modal COP values for a given
temperature bin
 They incorporate all transient effects including defrosting and
part load cycling (previous box plots were steady-state only)
DHP2
DHP3
7
7
6
6
6
5
5
5
4
4
4
3
COP
7
COP
COP
DHP1
3
2
2
2
1
1
1
0
0
0
15
20
40
60
Outdoor Temp (F)
10619
12095
13183
Predicted
13170
80
3
0
20
40
60
Outdoor Temp (F)
80
0
0
20
40
60
Outdoor Temp (F)
10564
10626
11279
11936
12321
11446
Predicted
12411
12322
Predicted
80
Multi-Zones with a Single-Zone Model?
 SEEM is a single zone heating simulation
 DHPs and ER zonal systems are, by definition, multizone
 Simulation implementation is to determine the
fraction of the entire house heated by the DHP
at every hour (DHPƒ). Then, fill in the remaining
heating requirement with resistance heat.
 Field measurements show DHPƒ depends
strongly on outdoor temperature and house
heat loss rate
16
DHPƒ Field Observations
Fraction of total metered heating provided by the ductless
heat pump
DHPƒ = (DHPheat) / (DHPheat + ERheat)
17
Multi-Zones with a Single-Zone Model
Logistic function used for DHPƒ curve fit within SEEM:

𝐷𝐻𝑃𝑓 =
OAT is outside temperature
UA is house heat loss
c1 and c2 are constants
from a regression fit.
18
1
1 + 𝑒 −(𝑐1∗𝑂𝐴𝑇+𝑐2∗𝑈𝐴)
Measured and Modeled Heating Energy
 SEEM can model both the base case houses
(ER heat only) and the post case houses (mix of
DHP and ER heating)
 Per other calibration efforts, house models constructed from detailed audit
data and the SEEM t-stat setting changed to match metered energy
Pre /
Post
DHP
Pre
Post
19
Source
Heating
Energy Use
(kWh/yr)
N
Mean
SD
Billing Data
9347
3892
91
SEEM 65.8°F Set point
9369
4111
91
SEEM 67.3°F Set point
10384
4409
91
Metered Data
6484
3894
91
SEEM 65.8°F Set point
5881
3018
91
SEEM 67.3°F Set point
6485
3234
91
Agreement: Metered Sites to Billing Sites
 95 metered sites are a subpopulation of the 4,000 billing
analysis sites
 Metered sites used no supplemental fuel and were continuously occupied year round
 When we examine the energy savings the billing population
would have were it to use no supplemental fuel and be fully
occupied, we see the same savings as from the meters and
simulation.
 Screened billing analysis savings: ~2,975 kWh/yr for 1706 houses
agrees well with calibrated modeled savings from previous slide of
2,865 kWh/yr for 91 sites.
 Link between metered and billing populations shows we can
expect SEEM to correctly simulate energy use under a variety of
conditions.
20
SEEM is Calibrated to Model Energy Use in Houses
with DHPs
 Sound Engineering & Statistical Analysis: Lab and field
measurements show us how the equipment performs
apart from the occupant.
 Reliable Data & Calibration: We can use the simulation
with confidence because it is calibrated and validated
against field data.
 Flexibility: The simulation of the equipment allows us to
model various program designs and occupant behaviors
giving the possibility to move beyond this pilot project
population.
21
Issue 2: How to determine electric kWh savings and
supplemental fuel benefit?
22
Distribution of Total DHP Savings
Electric Savings
Supplemental
Fuels
Takeback
23
Options for Supplemental Heat
Option 1: Electric kWh savings are based on results of the billing/metering studies (first-year);
supplemental fuel is quantified as found in the evaluation, and monetized.
 Analysis:



Uses billing analysis results from the pilot program
Uses savings that are consistent with supplemental fuel use across the region
Pros:

Reduces uncertainty in savings estimate




Potentially underestimates long-term savings
Increases risk that changing fuel preferences will increase electric baseline
Reduces savings estimate for homes without supplemental fuel use
May require differential savings based on supplemental fuel use
 Cons:
Option 2: Electric kWh savings are sum of first year savings and supplemental fuel savings
(long term = no wood use)
 Analysis:

Uses the results of detailed metering as the basis for savings calculation

Hedge against changing fuel preferences

May over estimate electric savings
 Pros:
 Cons:
Option 3: Somewhere in between Option 1 and 2; the percentage of long-term wood use is
based on ________.
 Pros:

Distributes uncertainty across short and long-term

May underestimate savings
 Cons:
24
Pilot Project Eligibility and Intake Screens
 Electric resistance (ER) heating must be permanently installed and serve
as the primary heating system for the home. (Screen for presence of ER;
no screen to establish ER as primary heat, meaning no screen for
wood/propane as de facto primary heat)
 The consumer must have occupied the home for one year prior. (In
addition, the consumer should expect to occupy the home for the next two
years.). (No screen for length of past/future occupancy)
 The consumer must allow their local utility to make their billing histories
available. (Included in terms of intake form)
 The consumer must agree to participate in the project, project activities,
and project evaluation. (Included in terms of intake form)
 Participating homes cannot:
 be new construction (No screen for new construction)
 have natural gas service to the home. (Screen for gas service)
25
Savings and Supplemental Fuels
Supplemental Fuels

 Documented in installation questionnaire
 Largely wood heat
 Some contractors did not ask about supplemental fuel
use (especially in some western climate areas)
 Dominated by rural participants
 Screened out of the metering sample (not
quantified)
 Supplemental fuels more significant in some
areas
 Rural areas of western climates.
 Most eastern climates (especially Montana)
26
Supplemental Fuel Use by Pilot Population*
Regional avg. = .35
27
*Based on data in Baylon, D., P. Storm, and D. Robison. 2013. Ductless Heat Pump Impact
& Process Evaluation: Billing Analysis Report, Northwest Energy Efficiency Alliance.
Portland OR.
Supplemental Fuel Impact
Supplemental fuel impacts can dominate savings estimates
 Electric savings impacted by supplemental fuels

 Generally Wood, some propane and other fuels


Differential wood use in eastern clusters
Uncertainty in use of supplemental heating
 Reduction in wood use implied by negative bill “savings”
 Screening suggests about 2000 kWh/yr savings reduction
between homes with and without supplemental fuels
 CDA regression used to assess the size of the supplemental fuel
and other takeback effects
 Supplemental fuel savings impact 400 kWh/yr across the entire pilot
program
 Savings impact 700 kWh in eastern utilities and 350 kWh in western utilities
Supplemental fuel is a occupant choice that does not effect
the “primary” electric heating system.
 Electric heating system remains in place
28
Space Heating Savings: Supplemental Fuels*
Willamette (n=547)
Puget Sound (n=247)
Coastal (n=95)
Cluster
Inland Empire (n=65)
Boise/Twin (n=29)
Eastern Idaho (n=30)
Tri-Cities (n=14)
Western Montana (n=68)
Total (n=1095)
29
*Based on screened billing analysis in Baylon, D., P. Storm, and D. Robison.
2013. Ductless Heat Pump Impact & Process Evaluation: Billing Analysis Report,
Northwest Energy Efficiency Alliance. Portland OR.
4000
3000
2000
1000
0
-1000
-2000
-3000
-4000
Savings Estimate (kWh/year; 90% confidence interval)
Space Heating Savings: No Supplemental Fuels*
4000
3000
2000
1000
0
-1000
-2000
-3000
-4000
Savings Estimate (kWh/year; 90% confidence interval)
Willamette (n=1454)
Puget Sound (n=454)
Coastal (n=138)
Cluster
Inland Empire (n=61)
Boise/Twin (n=63)
Eastern Idaho (n=51)
Tri-Cities (n=37)
Western Montana (n=37)
Total (n=2295)
30
*Based on screened billing analysis in Baylon, D., P. Storm, and D. Robison.
2013. Ductless Heat Pump Impact & Process Evaluation: Billing Analysis Report,
Northwest Energy Efficiency Alliance. Portland OR.
How to monetize supplemental fuels?
If supplemental fuel benefits are
included in the analysis (Option 1 and
3), how should they be monetized?
 Option A: Value of wood taken as the avoided cost of
wood fuel: Attempt to value wood directly.
 Option B: Value of wood taken as the avoided cost of
electricity: Use wholesale electricity prices.
 Option C: Value of wood taken as the cost of
electricity: Use retail electricity prices.
31
Issue 3: How/whether to include “comfort” in the measure
savings and/or TRC calculation?
32
Distribution of Total DHP Savings
Electric Savings
Supplemental
Fuels
Takeback
33
How/whether to include “comfort” in the measure
savings and/or TRC calculation?
Option 1: Do not include in analysis at all.
Option 2: Include in TRC analysis; convert to
$’s (benefit).
Option 3: Add to kWh savings.
34
Temperature and Comfort (MPER)
 Nearly all (97%) of respondents reported that
their home was more comfortable (91%) or
equally comfortable (6%) than it was prior to
installing the DHP.
 Only two respondents indicated that the
home was less comfortable.
 Respondents gave a variety of ways in which
their comfort was improved by the DHP.
35
Thermostat Settings and Setback (MPER)
 Pre and post-DHP avg. heating temp. reported at 69-70° F
 Pre-DHP, 69% reported setback when leaving the house or
at night; 23% said they never setback.
 Post-DHP, 42% reported setback when leaving the house
or at night; 35% said they never setback.
 57% said they were heating the same amount pre and
post-DHP, 40% said they were heating it more. The most
common reason given for heating the area more was that
the new heat was cheaper to operate (61%).
36
Savings with Temperature Setting Offsets
The DHP offers an improved thermostat control
and a reduction in heating energy.
 Reduced savings inferred from the temperature
observed in the metering.
 Regression suggests a 125 kWh savings reduction per ºF
 SEEM calibration suggested a temperature
adjustment.
 About 2 ºF increase in overall thermostat developed in the
calibration
 Billing analysis CDA showed other savings
offsets after supplemental fuels considered.
 Thermostat setting one possible source of takeback
37
Detailed interview: Metered Sample
Temperature changes from interviews for
metered sample

 20% said they increased temperature by
about 3ºF on average.
 9% said they decreased temperature by
about 3ºF on average.
 Relation between reported t-stat setting and
measured temperature suggests a higher
setting than reported by about 1ºF.
38
Inferred Temperature Impacts

Temperature impacts not directly observed
 Metering only included post installation
conditions
 No questions on heat setting
Indicator variable developed to track homes
with better heat signatures

 Increased R2 in post installation period
 Assigned indicator to the 40% largest increases
in R2save
 Most screened out with supplemental fuels
 Some screened out with pre installation R2 screening
 Screened savings “takeback” summaries based
on this variable
39
Space Heating Savings: No Takeback*
4000
3000
2000
1000
0
-1000
-2000
-3000
-4000
Savings Estimate (kWh/year; 90% confidence interval)
Willamette (n=1113)
Puget Sound (n=339)
Coastal (n=66)
Cluster
Inland Empire (n=43)
Boise/Twin (n=39)
Eastern Idaho (n=50)
Tri-Cities (n=31)
Western Montana (n=25)
Total (n=1706)
40
*Based on screened billing analysis in Baylon, D., P. Storm, and D. Robison.
2013. Ductless Heat Pump Impact & Process Evaluation: Billing Analysis Report,
Northwest Energy Efficiency Alliance. Portland OR.
Space Heating Savings: Temperature Increase
Indicator*
4000
3000
2000
1000
0
-1000
-2000
-3000
-4000
Savings Estimate (kWh/year; 90% confidence interval)
Willamette (n=342)
Puget Sound (n=115)
Coastal (n=72)
Cluster
Inland Empire (n=18)
Boise/Twin (n=24)
Eastern Idaho (n=1)
Tri-Cities (n=6)
Western Montana (n=12)
Total (n=590)
41
*Based on screened billing analysis in Baylon, D., P. Storm, and D. Robison.
2013. Ductless Heat Pump Impact & Process Evaluation: Billing Analysis Report,
Northwest Energy Efficiency Alliance. Portland OR.
“Takeback” Decisions
T-stat increases account for savings takeback
 SEEM predicts about 400 kWh/ºF
 Temperature take back up to 800 kWh/yr in metered
sample
 Bill screening suggests 650 kWh/yr per home with this
indicator
 CDA predicts 500 kWh/yr for homes with this indicator
Should these takebacks be included as part of the DHP
savings benefits?
 Option 1: Do not include in analysis at all.
 Option 2: Include in TRC analysis; convert to $’s (benefit).
 Option 3: Add to kWh savings.
42
Issue 4: Should we combine the savings, or disaggregate by
climate zone?
43
Use Similar DHP Savings Total: All climates

Similar installation standards in all climates
 Displacement model anticipates optimum output and cost
effectiveness in all climates.
 Installation standardized at 1-1.5 tons throughout the region
 Occupant use similar across region
 Supplemental fuel most significant determinant of savings in all
climates.
Evaluation of COP by climate shows similar response in
metered group
 Savings dominated by swing seasons in cold climates
 Savings available year round in warm climates
 Cooling not a significant offset in any climate
Average space heat fraction differs between western and
eastern climates but absolute saving similar
 Use of wood heating different between west and east so
uniform grid savings not expected
44
DHP Total Savings Results*
Willamette (n=18)
Cluster
Puget Sound (n=19)
Inland Empire (n=11)
Boise/Twin (n=8)
Eastern Idaho (n=9)
Total (n=65)
45
*Based on metered heat output measurements in Baylon, D., L. Larson, P. Storm,
and K. Geraghty. 2012. Ductless Heat Pump Impact & Process Evaluation: Field
Metering Report, Northwest Energy Efficiency Alliance. Portland OR.
6000
5000
4000
3000
2000
1000
0
Savings Estimate (kWh/year; 90% confidence interval)
Installations Similar Across Climates*
Capacity (tons)
Cluster
46
One Indoor Unit
All
Willamette
1.4
1.7
Puget Sound
1.3
1.6
Coastal
1.2
1.4
Inland Empire
1.7
1.9
Boise/Twin
1.3
1.8
Eastern Idaho
1.3
1.6
Tri-Cities
1.3
1.6
W. Montana
1.3
1.5
Total
1.4
1.6
*See Baylon, D., L. Larson, P. Storm, and K. Geraghty. 2012. Ductless Heat Pump
Impact & Process Evaluation: Billing Analysis Report, Northwest Energy Efficiency
Alliance. Portland OR.
Wood Heat Varies by Occupant not Climate*
Regional avg. = 393
47
*Based on conditional demand analysis (CDA) data in Baylon, D., P. Storm, and D. Robison.
2013. Ductless Heat Pump Impact & Process Evaluation: Billing Analysis Report, Northwest
Energy Efficiency Alliance. Portland OR.
DHP measure should be uniform, based on one
regional specification and savings.
 Total savings very uniform across climates.
 Supplemental fuels should be handled
separately in assigning “grid” savings.
 With common displacement spec common
savings should be anticipated.
 Climate distinction an unnecessary
complication.
48
Questions & Answers
49
Motions
50
Motion 1: Savings Estimation Approach
“I ____ move that the calibrated engineering
approach be used to estimate savings for
DHP measures and programs.”
51
Motion 2: Approach to Supplemental Fuels
“I _______ move to include supplemental heat
in the DHP savings estimate analysis using the
following option:
Option 1: First year savings approach. Electric kWh savings are
based on results of the billing/metering studies (first-year);
supplemental fuel savings is quantified as found in the
evaluation, and monetized.
Option 2: Long-term savings approach. Electric kWh savings are
sum of first year savings and supplemental fuel (long term = no
wood use)
Option 3: Hybrid approach. Somewhere in between Option 1 and
2; the percentage of long-term wood use is based on ______.
52
Motion 3: Approach to Takeback
“I _______ move to include or exclude
takeback offsets in final savings estimates.”
53
Motion 4: Uniform DHP Measure
“I _______ move to use a single savings
estimate for DHP total savings across all
climate zones.”
54
Additional Slides
55
Savings Vary by Screening Approach
Savings by Participant Group
Savings (kWh/yr)
Screened bills: R2>.45, Space Heat>0
Mean
EB
n
All
2081
81
3390
Supplemental Fuels Used
747
144
1095
No Supplemental Fuels Used
2719
90
2295
Takeback based on R2
1971
181
590
No Takeback
2976
101
1705
Metered Results: Measured Savings from Metered Sub-Sample
56
Total Savings (COP)
3887
375
65
Billing Analysis
3049
251
93
Performance Curves Compared
First 2 are for the units
tested in the lab and
cover a high HSPF range.
Third curve, based solely
on field data, developed
because we needed a
lower performing model.
The COP begins to bend
down at warmer
temperatures because of
equipment cycling.
57
CDA Billing Analysis Segmentation
 Assess the overall savings and the space heating
savings from the DHP installations in the pilot
project (n=3620)
 Determine the impact of takeback effects on
observed savings using CDA
 Underlying savings rate (c1) similar to meters
 Supplemental fuels offset (c2) consistent except
MT
 Constant term (C) shows impact of other
occupancy takebacks
58
CDA Regression Results
SHsaved=c1SHpre+c2SuppFuel+C
Parameter
Parameter
c
Parameter
Climate Zone
Segment
Climate
c
Zone
Est.
c1
SegmentZone
Climate
Western
0.479
Segment
Eastern*
0.219
Est.
W. Montana*
0.241
Western
All
0.426
Western
0.479
Eastern
Eastern*
0.219
W. Montana
W.
Montana*
0.241
All
All
0.426
59
1
C
2
EB
0.016
Est.
-1078
EB
c2
131
c456
2
Est.
-676
c0.046
1
-1220
-226
EB
Est.
EB
0.096
-1761
1263
-275
0.487
-973
0.015
-1208
129
-466
0.016
-1078
131
0.223
-1,152
0.046
-1220
456
0.249
-1,683
0.096
-1761 1263
0.434
-1,110
0.015
-1208
129
EB
140
C
n
3,122
C519
n
375
Est.
EB
n
1545
123
-768 3,620
3122
139
-676
140 3,122
-300
375
-226
519
375
-416
123
-275 1545
123
-561
3620
-466
139 3,620
CDA Savings Estimates
CDA savings estimates similar to the
screened billing analysis results

 Supplemental fuel decrements the total
savings by about 1200 kWh/yr in those
homes
 Other “Takeback” captured by constant term
 Regression did not include R2 indicator
 Screening results suggest about a third of the
constant effect is explained by this indicator
 Overall savings represents the comparable
screening to the metered sample
60
Segmented Regression Results
61
CDA Predicted Space Heating Savings
Willamette (n=2086)
Puget Sound (n=752)
Coastal (n=285)
Cluster
Inland Empire (n=140)
Boise/Twin (n=96)
Eastern Idaho (n=84)
Tri-Cities (n=55)
Western Montana (n=123)
Total (n=3621)
62
4000
3000
2000
1000
0
-1000
-2000
-3000
-4000
Savings Estimate (kWh/year; 90% confidence interval)
The CDA comparison
Overall savings from the CDA equivalent to screened
billing analysis
 Based only on space heat coefficient (c1)
 Comparable to Metered Sample billing savings
Overall “takeback” from all sources equal to a third of
predicted savings
 Supplemental fuels account for 40% of that
reduction
 Temperature “takeback” accounts for about 25% of
that reduction
 The balance is the result of occupancy or other
behavior
How should these effects be included in the
cost/effectiveness analysis?
63
Savings and C/B Recommendations
 Supplemental fuel taken as the value of the
offset electric heat
 Temperature and occupancy effects should
be ignored
 Total savings should be used for TRC cost
effectiveness
 Based on the c1 coefficient
 c1= .48 for western climates
.24 for eastern climates
 Grid Savings would account for observed
takeback especially supplemental fuels
64
Modeled and Measured COP
65
Average/Total Eastern Idaho
(n=69)
(n=9)
Boise/Twin
(n=8)
Inland Empire Puget Sound
(n=12)
(n=20)
Willamette
(n=20)
2
SEEM Modeled
Metered
SEEM Modeled
Metered
SEEM Modeled
Metered
SEEM Modeled
Metered
SEEM Modeled
Metered
SEEM Modeled
Metered
2.5
COP (90% confidence interval)
3
3.5
4