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Quality control for irrigation data. Most farmers budget
Chapter 13, Problem 14E(choose chapter or problem)
Quality control for irrigation data. Most farmers budget water by using an irrigation schedule. The success of the schedule hinges on collecting accurate data on evapotranspiration (ETo), a term that describes the sum of evaporation and plant transpiration. The California Irrigation Management Information System (CIMIS) collects daily weather data (e.g., air temperature, wind speed, and vapor pressure) used to estimate ETo and supplies this information to farmers. Researchers at CIMIS demonstrated the use of quality-control charts to monitor daily ETo measurements (IV International Symposium on Irrigation of Horticultural Crops, Dec. 31, 2004). Daily minimum air temperatures (\(^{\circ}C\)) collected hourly during the month of May at the Davis CIMIS station yielded the following summary statistics (where five measurements are collected each hour): \(\overline{\bar{x}}=10.16^{\circ} \text { and } R=14.87^{\circ}\).
a. Use the information provided to find the lower and upper control limits for an \(\bar{x}\)-chart.
b. Suppose that one day in May the mean air temperature at the Davis CIMIS station was recorded as \(\bar{x}=20.3^{\circ}\). How should the manager of the station respond to this observation?
Questions & Answers
QUESTION:
Quality control for irrigation data. Most farmers budget water by using an irrigation schedule. The success of the schedule hinges on collecting accurate data on evapotranspiration (ETo), a term that describes the sum of evaporation and plant transpiration. The California Irrigation Management Information System (CIMIS) collects daily weather data (e.g., air temperature, wind speed, and vapor pressure) used to estimate ETo and supplies this information to farmers. Researchers at CIMIS demonstrated the use of quality-control charts to monitor daily ETo measurements (IV International Symposium on Irrigation of Horticultural Crops, Dec. 31, 2004). Daily minimum air temperatures (\(^{\circ}C\)) collected hourly during the month of May at the Davis CIMIS station yielded the following summary statistics (where five measurements are collected each hour): \(\overline{\bar{x}}=10.16^{\circ} \text { and } R=14.87^{\circ}\).
a. Use the information provided to find the lower and upper control limits for an \(\bar{x}\)-chart.
b. Suppose that one day in May the mean air temperature at the Davis CIMIS station was recorded as \(\bar{x}=20.3^{\circ}\). How should the manager of the station respond to this observation?
ANSWER:
Step 1 of 2
Here we collected the data hourly during the month of May at the Davis CIMIS station
and we get the summary statistics as follows:
Also we have informed that 5 measurements are collected each hour. That means n = 5.
a) According to 
By definitions, the upper and lower control limits are defined as
Using control chart constants table, We observe 
n = 5 .
Therefore,
