Chapter 7, Survey Sampling

Solution 20

Since is a fixed number it does not make sense that . Just to make it clear - probability means that there is a range/set of values that a random variable can take. Here the population mean is a fixed value, thus it does not make sense to say .

The confidence interval means that 95% of the confidence intervals formed in this way contains . Or there is a 95% chance that this interval contains but it does not say that the probability that takes one of the values in the interval is . The value of is fixed and it does not take any values from the interval! It’s the interval that we say that the chance that this interval containing the value of is 95% because intervals are random and the interval we formed in this way have the probability for containing is 95%.

The confidence interval says about the probability of the interval not of the population mean.

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