In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.


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Notation Identify the values of n1,n2 and G that would be used in the runs test for randomness.

Verified step by step guidance

1. Step 1: Understand the problem. The runs test for randomness is a non-parametric statistical test used to determine if a sequence of data points is random. In this case, the sequence consists of political party affiliations (R for Republican and D for Democrat). The goal is to identify the values of n1 (number of R's), n2 (number of D's), and G (number of runs).
2. Step 2: Count the occurrences of R and D in the sequence. To find n1, count the total number of R's in the sequence. Similarly, to find n2, count the total number of D's in the sequence. These values represent the frequency of each category in the sequence.
3. Step 3: Define a 'run' in the context of the sequence. A run is a consecutive sequence of the same symbol (either R or D). For example, if the sequence is RRRDDRR, there are three runs: one of R's, one of D's, and another of R's.
4. Step 4: Count the total number of runs (G) in the sequence. To do this, examine the sequence and identify where the symbol changes from R to D or D to R. Each change marks the end of one run and the beginning of another.
5. Step 5: Summarize the values. After counting n1, n2, and G, these values can be used in the runs test formula to assess randomness. Ensure the counts are accurate and clearly documented for further analysis.

Key Concepts

Runs Test

The Runs Test is a non-parametric statistical test used to determine the randomness of a sequence of data. It analyzes the occurrence of runs, which are sequences of similar items, to assess whether the order of the items is random or exhibits a pattern. In the context of political party affiliations, it helps to evaluate if the sequence of 'R' and 'D' affiliations is random or shows a preference for one party over the other.

n1 and n2

In the context of the Runs Test, n1 and n2 represent the number of occurrences of each category in the sequence being analyzed. For example, n1 could denote the number of Republicans (R) and n2 the number of Democrats (D) in the given sequence. These values are essential for calculating the expected number of runs and determining the test's significance.

G (Number of Runs)

G, or the number of runs, is a key statistic in the Runs Test that counts the total number of uninterrupted sequences of similar items in the data. A run is defined as a sequence of consecutive identical elements, such as a series of 'R's followed by 'D's. The value of G is compared against expected values to assess whether the observed runs indicate randomness or a systematic pattern in the data.