BUS 223 Lecture Notes - Lecture 12: Coffee Vending Machine, Confidence Interval, Point Estimation
25 Jun 2018
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STATISTICAL ESTIMATION
• STATISTICAL INFERENCE is the process by which statisticians make
predictions about a population on the basis of samples
• STATISTICAL ESTIMATION is the use of sample data to estimate certain
unknown quantities of the population
POINT ESTIMATE
• A single number used to describe something. The mean is a point estimate
that is used to describe a sample or population.
• To increase our confidence in this estimate we could increase the size of the
sample.
• To increase our confidence we could use a range of numbers to describe a
value.
ESTIMATING THE POPULATION MEAN ON THE BASIS OF A LARGE
SAMPLE
• Decide on the level of confidence needed to accomplish the task.
• Using Central Limit Theory, construct our confidence levels on a normal
graph
• Confidence intervals are always two tailed in order to represent a value less
than and a value greater than the point estimate (mean of the sample)
• Using the normal distribution tables, calculate the Z-score for the above.
• Use the formula to calculate the range of numbers that will estimate the
value of the population mean to the desired level of confidence.
DETERMINING THE SAMPLE SIZE
• The size of the sample is determined by the desired degree of accuracy.
• Accuracy is determined by looking at the MAXIMUM ALLOWABLE
ERROR and the CONFIDENCE we have that our maximum allowable error
will be to the true value.
• In order to estimate the sample size we must know the maximum allowable
error and the degree of confidence required.
• Using Central Limit Theory, find the Z-score, and using the formula
provided, estimate the size of the sample.
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Document Summary
Statistical estimation: statistical inference is the process by which statisticians make predictions about a population on the basis of samples, statistical estimation is the use of sample data to estimate certain unknown quantities of the population. Point estimate: a single number used to describe something. Estimating the population mean on the basis of a large. Determining the sample size: the size of the sample is determined by the desired degree of accuracy, accuracy is determined by looking at the maximum allowable. Examples: a coffee vending machine fills 100 cups of coffee before it has to be refilled. On monday the mean number of ounces in a filled cup of coffee was 7. 5 ounces. The population standard deviation is known to be 0. 25 ounces. Find the 95% confidence interval for the mean number of ounces of coffee dispensed by this machine: a sample survey of 81 movie theaters showed that the average length of a feature film was 90 minutes.
