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


n=415, pᵢ=0.08

Verified step by step guidance

1. Identify the formula for calculating the expected frequency: Expected Frequency (E) = n × pᵢ, where n is the total number of observations and pᵢ is the probability of the specific category.
2. Substitute the given values into the formula. Here, n = 415 and pᵢ = 0.08.
3. Perform the multiplication: Multiply 415 by 0.08 to calculate the expected frequency.
4. Interpret the result: The expected frequency represents the number of occurrences you would expect in the specific category based on the given probability and total observations.
5. Ensure the result is reasonable: Verify that the expected frequency is a positive value and makes sense in the context of the problem.

Key Concepts

Expected Frequency

Expected frequency is a statistical term that refers to the anticipated number of occurrences of an event in a given sample size, based on a specific probability. It is calculated by multiplying the total number of observations (n) by the probability of the event (pᵢ). In this case, with n=415 and pᵢ=0.08, the expected frequency can be found by calculating 415 * 0.08.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. A probability of 0 indicates that the event will not occur, while a probability of 1 indicates certainty. In the context of this question, pᵢ=0.08 signifies that there is an 8% chance of the event happening in any given trial.

Sample Size

Sample size refers to the number of observations or data points collected in a study or experiment. It is crucial for determining the reliability and validity of statistical results. In this question, n=415 indicates that the analysis is based on 415 observations, which influences the calculation of expected frequencies and the overall statistical inference.