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# Statistics Module 3: Understanding Inference

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• Statistics Module 3: Understanding Inference

Module 3 includes a brief overview of random sampling and introduces the concept of confidence interval. The sampling concept is important to understand the distinction between population and sample statistic. Sample statistic like point estimates are numerical values like mean, standard deviation and variance calculated from the samples of a population. Sampling is of various types.

Interval estimates like confidence interval are used to capture the population parameter within a certain range. Samples from same population with a fixed sample size are plotted and follow a normal distribution. The mean of the sample distribution is the population mean.

Standard Error of the mean

Standard error of the mean is the variance of point estimates from the population mean. Its calculated by dividing standard deviation of an independent population with square root of sample size. Standard error reduces with increase in the sample size. As thump rule, sampling size should be less than 10 percent of the population for it to be independent with sample size equal or greater than 30.

Confidence Interval C.I.

C.I. capture probability of population parameter within a certain range. It shares the likelihood of an unknown population parameter to fall within a certain range. Random samples are used to estimate population mean. Example a 90% Confidence Interval means that 90% of the time the sample distribution of the mean contains the population mean.

• α level of significance Example 5%
• 1- α degree of confidence corresponding C.I  95%

A good way of interpreting confidence interval is as follows. For the above mentioned C.I of 95%.

I am 95% confidence that the population parameter lies between the range from ____ to ________.

Margin of Error

Margin of error multiplies Z statistic for a given probability with sampling error or standard error. The tutorial includes solved problems related to the topic along with the excel download included in the data analysis sheet here.