### 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! Itâ€™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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