Question

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

Answer 1

It is necessary to check whether the population is approximately normal before constructing a confidence interval because it is germane to show that data near the mean are more frequent in occurrence than data far from the mean.

Explanation:

The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.

The Kolmogorov-Smirnov test (K-S) and Shapiro-Wilk (S-W) test are designed to test normality by comparing your data to a normal distribution with the same mean and standard deviation of your sample. If the test is NOT significant, then the data are normal, so any value above . 05 indicates normality.

Steps to determine if sampling distribution is normal?

• If the population is skewed, then the sample mean won't be normal for when N is small.
• If the population is normal, then the distribution of sample mean looks normal even if N = 2.
• If the population is skewed, then the distribution of sample mean looks more and more normal when N gets larger.

Confidence Interval -

In statistics, a confidence interval (CI) is a type of estimate computed from the statistics of the observed data. This proposes a range of plausible values for an unknown parameter (for example, the mean). The interval has an associated confidence level that the true parameter is in the proposed range.

Answer 2

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

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.