Youtube Full Course: Test of Hypothesis

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Hello,

 Full video course is now available on Youtube

 Visit my dedicated channel here >> Test of Hypothesis


All the best with your learning journey :)

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The Fact and the Hypothesis

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A good fact to submit is that we can't easily know the exact truth values/parameters of a population. Mostly, population parameters also change slightly by time and/or affected by different surrounding factors. Example: a production line for the 500 ml bottles is assumed to produce a population of bottles such that mean value of bottles capacity is exactly 500 ml. Nice, but what happens in realty? In realty, several factors will mostly affect the production: human factors, machine factors, environment temperature...etc. Also, each new bottle will contribute in the population mean value. This means a continuous slight change, either up or down, of the mean capacity. Here comes the hypothesis! As you see, the ground truth value for population mean is difficult to be exactly determined. However, we have general assumptions/expectations. OK, constructing a hypothesis should always be driven by our initial knowledge and expectations about the population. ...
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Confidence Level and Confidence Interval

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Being confident make one's self more reassured. Briefly, explanations below are for two sided confidence levels/intervals in order to simplify the idea. Saying " two sided " gives initial impression that there is something like two limits, yeah they are: upper and lower limits where the confidence interval lies in between. Example: Let's look at the population of a specific mobile phone model. Suppose we are now interested in the ' weight ' property. We found that weight property follows a normal distribution with mean value of 120 grams and a standard deviation of 1.4 grams. Weight ~ Normal (Mu, Sigma) = Normal (120, 1.4) This understanding means that majority of mobiles tested will weigh very closely to 120 grams. Yes, there should be fluctuations above and below the mean value but surely that still relatively close to mean value. Suppose a question: do you expect weights like: 121, 119.5, 122.1, 118.9? Answer: Yes , I surely expect such ...
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Understanding the distribution of sample mean (x_bar)

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Cool, say now we have a huge population with characteristics ( Mu, Sigma^2 ). When doing a study by sampling, we take a random sample ( size n items ) and then perform the study on the sample and conclude results back for the population. From Central Limit Theorem, we know that the sample mean will always follow a normal distribution  apart from what the population distribution is, such that: x_bar ~ N (Mu, Sigma^2/n) or say: Expected (x_bar) = Mu Variance (x_bar) = Sigma^2/n Well, let's see a simple illustrating example: Suppose we have a population with mean Mu=100 . Now, we have taken a sample, and computed the sample mean, x_bar. We mostly will have x_bar near 100 but not exactly 100. OK, let take another 9 separate samples... suppose these results: First sample --> x_bar = 99.8 Second sample --> x_bar = 100.1 .. .. .. 10th sample --> x_bar = 100.3 What we see that the sample mean is usually...
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