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Chapter 6: Q3 (page 281)

Small Sample Data set 29 鈥淐oin Weights鈥� in Appendix B includes weights of 20 one-dollar coins. Given that the sample size is less than 30, what requirement must be met in order to treat the sample mean as a value from a normally distributed population? Identify three tools for verifying that requirement.

Short Answer

Expert verified

It is important to verify that the sample is from a population that follows a normal distribution.

The following three tools can be applied to check the normality of the data:

  • Construction of the histogram
  • Construction of the normal quantile plot
  • Identification of outliers

Step by step solution

01

Given information

A sample of weights of 20 one-dollar coins is considered.

02

Examining normality of the data

It is given that the sample of weights of one-dollar coins is considered.

The sample size is equal to 20, which is less than 30.

Since the sample size is less than 30, the sample cannot be considered a normally distributed population unless the distribution is examined/tested.

The requirement that must be fulfilled is that the sample observations must be from a normally distributed population.

The following three tools can be utilized to test whether the sample comes from a normally distributed population or not:

  • A histogram of the sample values can be plotted. The sample is from a normally distributed population if the histogram is approximately bell-shaped.
  • A normal quantile plot of the sample values can be plotted.The sample is from a normally distributed population if the plot consists of points that follow a straight-line pattern.
  • Outliers, if present, can be identified. If the number of outliers present is more than one, the sample is not from a normally distributed population.

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