Question

For a sample from a normally distributed population, which of the following statements is false?


Question 4 options:

The distribution of frequencies in the sample data tends to follow the same bell-shaped curve as the underlying distribution.


The larger the sample, the more reliably it will reflect the population.


Continuity correction should be used when continuous data are being modelled.


The sample mean and sample standard deviation, provide estimates of the population parameters

Answer 1

Answer:

The normal distribution is simply a distribution with a certain shape. It is normal because many things have this same shape. The normal distribution is the bell-shaped distribution that describes how so many natural, machine-made, or human performance outcomes are distributed. If you ever took a class when you were “graded on a bell curve”, the instructor was fitting the class’s grades into a normal distribution—not a bad practice if the class is large and the tests are objective, since human performance in such situations is normally distributed. This chapter will discuss the normal distribution and then move on to a common sampling distribution, the t-distribution. The t-distribution can be formed by taking many samples (strictly, all possible samples) of the same size from a normal population. For each sample, the same statistic, called the t-statistic, which we will learn more about later, is calculated. The relative frequency distribution of these t-statistics is the t-distribution. It turns out that t-statistics can be computed a number of different ways on samples drawn in a number of different situations and still have the same relative frequency distribution. This makes the t-distribution useful for making many different inferences, so it is one of the most important links between samples and populations used by statisticians. In between discussing the normal and t-distributions, we will discuss the central limit theorem. The t-distribution and the central limit theorem give us knowledge about the relationship between sample means and population means that allows us to make inferences about the population mean.