[DATA] Walt Disney Stock The table shows the movement of Walt Disney stock for 30 randomly selected trading days. “Up” means the stock price increased in value for the day. “Down” means the stock price decreased in value for the day, and “No Change” means the stock price closed at the same price it closed for the previous day.
e. Would the estimate of the probability of Walt Disney stock price movement improve if we considered 60 randomly selected days instead? Explain.

Verified step by step guidance

1. Step 1: Understand the problem context. We are estimating the probability of Walt Disney stock price movements (Up, Down, No Change) based on observed data from 30 randomly selected trading days.
2. Step 2: Recall that the estimate of probability for an event is calculated as the relative frequency of that event in the sample. For example, the probability of 'Up' is estimated as \(\frac{\text{Number of 'Up' days}}{\text{Total number of days}}\).
3. Step 3: Consider the effect of sample size on the estimate. Larger sample sizes tend to provide more reliable and stable estimates of probabilities because they reduce the impact of random fluctuations or outliers.
4. Step 4: Explain that increasing the sample size from 30 to 60 days would likely improve the estimate of the probability because it would better represent the true distribution of stock movements over time.
5. Step 5: Conclude that with 60 randomly selected days, the estimate of the probability would be more accurate and less variable, leading to a better understanding of the stock's behavior.

Key Concepts

Probability Estimation

Probability estimation involves calculating the likelihood of an event based on observed data. In this context, it means estimating the chance of the stock moving Up, Down, or having No Change by dividing the frequency of each outcome by the total number of observed days.

Law of Large Numbers

The Law of Large Numbers states that as the number of trials or observations increases, the estimated probability tends to get closer to the true probability. Therefore, using 60 days instead of 30 days would likely provide a more accurate and stable estimate of stock movement probabilities.

Random Sampling

Random sampling ensures that each day’s stock movement is selected without bias, making the sample representative of the overall population. This is crucial for valid probability estimates, as non-random samples can lead to misleading conclusions about stock behavior.