Final answer:
True, an R chart tracks the variability within a sample by measuring the range of the data. For making predictions with a linear trend, it is necessary for the correlation coefficient to be significant and the trend to be linear within the observed domain. When performing hypothesis tests with matched or paired samples, it is true that the measurements come from the same pair and that two sample means are compared.
Step-by-step explanation:
An R chart, also known as a range chart, is indeed used to track how much the individual observations within a sample vary. The purpose of the R chart is to monitor the process variability, which is reflected by the difference in the range of the data. This type of chart is particularly important in quality control processes where consistency is critical. However, it should not be confused with tracking central tendency, which is done using an X-bar chart.
When it comes to making predictions using a linear trend from a scatter plot, it is true that if the correlation coefficient (r) is significant and the scatter plot indicates a linear relationship, the derived line can be used to predict the value of y for values of x within the domain of observed x values. For the predictions to be reliable, it is important that r is significant and the data does indeed have a linear trend.
In hypothesis testing, particularly with matched or paired samples, statements B and D are true. Matched samples indicate that two measurements are drawn from the same pair of individuals or objects, and indeed two sample means are compared to each other. The idea that sample sizes in matched samples are almost never small is not necessarily true; matched samples can be of any size.
The statement that if the null hypothesis is false, the variance of the combined data is larger is true. Variance is a measure of variability, and significant differences in means between groups will contribute to increased variability. In other words, if there are differences (i.e., one mean is higher than the other), it's likely that the data will spread out more, and thus the variance will be larger.