In Exercises 17–24, use the indicated Data Sets from Appendix B. The complete data sets can be found at www.TriolaStats.com. Assume that the paired sample data are simple random samples and the differences have a distribution that is approximately normal.


Heights of Presidents Repeat Exercise 12 “Heights of Presidents” using all of the sample data from Data Set 22 “Presidents” in Appendix B.

Verified step by step guidance

1. Step 1: Identify the paired sample data from Data Set 22 'Presidents' in Appendix B. Ensure that the data represents heights of presidents and is a simple random sample.
2. Step 2: Verify that the differences between paired samples have a distribution that is approximately normal. This can be done using graphical methods like a histogram or a normal probability plot, or by conducting a normality test such as the Shapiro-Wilk test.
3. Step 3: Calculate the differences between the paired sample data points. For each pair, subtract the height of one president from the height of the other to obtain the differences.
4. Step 4: Compute the mean and standard deviation of the differences. Use the formulas for mean (\( \text{Mean} = \frac{\sum x}{n} \)) and standard deviation (\( \text{SD} = \sqrt{\frac{\sum (x - \text{Mean})^2}{n-1}} \)) where \( x \) represents the differences and \( n \) is the number of pairs.
5. Step 5: Use the calculated mean and standard deviation of the differences to perform the required statistical analysis, such as constructing a confidence interval or conducting a hypothesis test, depending on the specific requirements of Exercise 12.

Key Concepts

Paired Samples

Paired samples refer to two sets of related data points where each observation in one sample is paired with a corresponding observation in the other sample. This design is often used in experiments where the same subjects are measured under different conditions, allowing for a direct comparison of the effects of those conditions.

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, indicating that data near the mean are more frequent in occurrence than data far from the mean. In statistics, many tests assume that the data follows a normal distribution, especially when sample sizes are small, as it allows for the application of various inferential statistical methods.

Simple Random Sampling

Simple random sampling is a fundamental sampling technique where each member of a population has an equal chance of being selected. This method helps to ensure that the sample is representative of the population, reducing bias and allowing for valid statistical inferences to be made from the sample data.