"[DATA] A Random Process: Green Lights On your drives to school each day you feel like there is a light that is always red when you reach it. You decide to record data to determine the likelihood of arriving at the light while it is red. Open the data set 5_1_38 at www.pearsonhighered.com/sullivanstats, which contains the day number and whether the light was red (1), or not (0), for 120 consecutive days in which you drove to school.
b. What proportion of the days were you stuck by a red light after 15 days?"

Verified step by step guidance

1. Identify the variable of interest, which is whether the light was red (coded as 1) or not (coded as 0) for each day.
2. Focus on the data for the first 15 days from the dataset, specifically the values corresponding to days 1 through 15.
3. Count the number of days within these 15 days where the light was red (i.e., the number of 1s in the data for these days).
4. Calculate the proportion of days with a red light by dividing the count of red light days by the total number of days considered (which is 15). This can be expressed as: \(\text{Proportion} = \frac{\text{Number of days with red light}}{15}\)
5. Interpret this proportion as the likelihood or probability of encountering a red light on any given day within the first 15 days.

Key Concepts

Proportion

Proportion is a measure that represents the fraction of times an event occurs relative to the total number of observations. In this context, it is the number of days the light was red divided by the total days observed. Proportions range from 0 to 1 and can be expressed as percentages for easier interpretation.

Binary Data

Binary data consists of observations with only two possible outcomes, such as red light (1) or not red light (0). This type of data is useful for calculating proportions and probabilities because each trial results in a simple yes/no or success/failure outcome.

Data Summarization and Interpretation

Data summarization involves organizing and condensing raw data to extract meaningful information, such as calculating the proportion of red light occurrences in the first 15 days. Interpretation means understanding what this proportion tells us about the likelihood of encountering a red light during those days.