1305AFE Lecture Notes - Lecture 8: Microsoft Powerpoint, Cubic Metre, Interval Estimation
Week 8 Business Data Analysis Lecture Notes
Statistical Inference
• Statistical inference is the process by which we acquire information about
populations from samples.
Estimation (Part 1)→ Point and Interval Estimates → Selecting the Sample Size
Estimation
• Point Estimator
o One value is calculated from the sample to infer the population
• Interval Estimator
o An interval of values is calculated from the sample to infer the population.
o Hope that this interval includes the population parameter
Point Estimator
• Single estimator allowing no margin for error taken at a given point in time
• is a point estimator of µ
• is a point estimator of p
• s is a point estimator of �
• Point Estimate is a value calculated from sample data, using the formula of a point
estimator.
Deficiencies of Point Estimator
• Point estimators do not include information about
• Its distance from the true value (population parameter)
• variance of the point estimator
• distribution of the point estimator
• On the other hand, an interval estimator takes into account of the variance and the
distribution of the estimator.
x
p
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Construct and Interval Estimate
• An interval estimate, called a confidence interval allows a margin for sampling error
to be incorporated with the point estimate
Interval Estimator
• An interval estimator draws inferences about a population by estimating the value of
an unknown population parameter using an interval.
• The interval estimator is affected by the sample size.
Confidence Interval Estimate of the Population Mean µ, when �2 is Known
• From the knowledge of the sampling distribution of the sample mean,
• There are two cases
Refer to Power Point Handout
X
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Statistical inference: statistical inference is the process by which we acquire information about populations from samples. Estimation (part 1) point and interval estimates selecting the sample size. Estimation: point estimator, one value is calculated from the sample to infer the population. Interval estimator: an interval of values is calculated from the sample to infer the population, hope that this interval includes the population parameter. Construct and interval estimate: an interval estimate, called a confidence interval allows a margin for sampling error to be incorporated with the point estimate. Interval estimator: an interval estimator draws inferences about a population by estimating the value of an unknown population parameter using an interval, the interval estimator is affected by the sample size. Confidence interval estimate of the population mean , when 2 is known: from the knowledge of the sampling distribution of the sample mean, Theoretical interpretation of confidence interval: example: interpret 90% confidence interval for the population mean m.
