Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval. It is necessary to check whether the population is approximately normal because

Yes, to construct a confidence interval, it is necessary to check whether the population is approximately normal or not.

Step-by-step explanation:

The information about distribution of population is important in order to find out the sampling distribution. When we want to construct confidence interval, the accuracy of results depend on three conditions.

1. The data needs to be randomly selected.

2. The sampling distribution needs to be normally distributed

3. The observations must be independent.

So one of the conditions is to ensure that the population is normally distributed.

We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10

np ≥ 10

n(1 - p) ≥ 10

When the population follows normal distribution then a small number of samples will be adequate, on the other hand, if the population is skewed then we need a greater sample size to ensure normal sampling distribution.  

Therefore, it is necessary to check whether the population is approximately normal before constructing a confidence interval.

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step-by-step explanation:

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