Finding Expected Frequencies
In Exercises 3–6, find the expected frequency for the values of n and pᵢ.


n=230, pᵢ=0.25

Verified step by step guidance

1. Step 1: Understand the concept of expected frequency. Expected frequency is calculated using the formula: E = n × pᵢ, where 'n' is the total number of observations and 'pᵢ' is the probability of the specific category or event.
2. Step 2: Identify the values given in the problem. Here, n = 230 (total number of observations) and pᵢ = 0.25 (probability of the specific category).
3. Step 3: Substitute the values into the formula for expected frequency. Using MathML, the formula is: $E=n\times p_i$. Substituting, it becomes: $E=230\times 0.25$.
4. Step 4: Perform the multiplication operation to calculate the expected frequency. Multiply 230 by 0.25 to find the result.
5. Step 5: Interpret the result. The expected frequency represents the number of occurrences you would expect for the specific category given the total observations and probability.

Key Concepts

Expected Frequency

Expected frequency refers to the anticipated number of occurrences of a particular outcome in a statistical experiment, calculated by multiplying the total number of trials (n) by the probability of the outcome (pᵢ). In this case, it helps in determining how many times we expect a specific event to happen based on the given probability.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In the context of this question, pᵢ represents the probability of a specific outcome occurring in a sample of size n, which is crucial for calculating expected frequencies.

Sample Size (n)

Sample size (n) is the total number of observations or trials in a statistical study. It is essential for determining the expected frequency, as a larger sample size can lead to more reliable estimates of probabilities and outcomes, thereby affecting the expected frequency calculation.