Comparing the Stock Performance of Apple and Microsoft You will compare the stock price performance of Apple (AAPL) and Microsoft (MSFT) over the year from January 1, 2023, to December 31, 2023, to determine if there's a statistically significant difference in their average daily stock prices and return. This allows us to test if there’s a significant difference in their stock prices and return over the entire year. Hypothesis: Null Hypothesis (H₀): There is no significant difference between the average daily stock returns of Apple and Microsoft over the year. Alternative Hypothesis (): There is a significant difference between the average daily stock returns of Apple and Microsoft over the year. Set the Null and Alternative Hypothesis mathematically Collect Stock Data using “STOCKHISTORY” function: Apple’s stock prices (AAPL): =STOCKHISTORY("AAPL", "2023/01/01", "2023/12/31",0,2,0,1) This will give you Apple’s daily closing stock prices from January 1, 2023, to December 31, 2023. Microsoft’s stock prices (MSFT): =STOCKHISTORY("MSFT", "2023/01/01", "2023/12/31",0,2,0,1) This will give you Microsoft’s daily closing stock prices for the same period. Calculate the Average Stock Prices and Average Daily Return: You can now calculate the average stock prices and daily return for both companies over the selected 12-month period. Calculate the average stock price of Apple: Calculate the average stock price of Microsoft: Calculate the average daily return of Apple: Calculate the average daily return of Microsoft: Set the Significance Level: Choose a significance level (α = 0.05), meaning you accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is true). Run a t-Test to Compare the Stock Prices: Now, perform a t-Test in Excel to compare the average stock return prices of the two companies. Interpret the Results: The T.TEST function will return a p-value: If the p-value ≤ 0.05, you reject the null hypothesis and conclude that there is a significant difference between the average stock prices of Apple and Microsoft. If the p-value > 0.05, you fail to reject the null hypothesis, meaning there is no statistically significant difference between their stock prices. Analyzing the Results: p-value from T.TEST: Decision based on hypothesis testing: Would you reject or fail to reject the null hypothesis? Interpretation: Is there a significant difference in the average stock prices and returns of Apple and Microsoft over the last year? Attach the Excel Output Here:

Comparing the Stock Performance of Apple and Microsoft You will compare the stock price performance of Apple (AAPL) and Microsoft (MSFT) over the year from January 1, 2023, to December 31, 2023, to determine if there's a statistically significant difference in their average daily stock prices and return. This allows us to test if there’s a significant difference in their stock prices and return over the entire year. Hypothesis: Null Hypothesis (H₀): There is no significant difference between the average daily stock returns of Apple and Microsoft over the year. Alternative Hypothesis (): There is a significant difference between the average daily stock returns of Apple and Microsoft over the year. Set the Null and Alternative Hypothesis mathematically Collect Stock Data using “STOCKHISTORY” function: Apple’s stock prices (AAPL): =STOCKHISTORY("AAPL", "2023/01/01", "2023/12/31",0,2,0,1) This will give you Apple’s daily closing stock prices from January 1, 2023, to December 31, 2023. Microsoft’s stock prices (MSFT): =STOCKHISTORY("MSFT", "2023/01/01", "2023/12/31",0,2,0,1) This will give you Microsoft’s daily closing stock prices for the same period. Calculate the Average Stock Prices and Average Daily Return: You can now calculate the average stock prices and daily return for both companies over the selected 12-month period. Calculate the average stock price of Apple: Calculate the average stock price of Microsoft: Calculate the average daily return of Apple: Calculate the average daily return of Microsoft: Set the Significance Level: Choose a significance level (α = 0.05), meaning you accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is true). Run a t-Test to Compare the Stock Prices: Now, perform a t-Test in Excel to compare the average stock return prices of the two companies. Interpret the Results: The T.TEST function will return a p-value: If the p-value ≤ 0.05, you reject the null hypothesis and conclude that there is a significant difference between the average stock prices of Apple and Microsoft. If the p-value > 0.05, you fail to reject the null hypothesis, meaning there is no statistically significant difference between their stock prices. Analyzing the Results: p-value from T.TEST: Decision based on hypothesis testing: Would you reject or fail to reject the null hypothesis? Interpretation: Is there a significant difference in the average stock prices and returns of Apple and Microsoft over the last year? Attach the Excel Output Here:

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section: Chapter Questions

Problem 6RP

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Comparing the Stock Performance of Apple and Microsoft

You will compare the stock price performance of Apple (AAPL) and Microsoft (MSFT) over the year from January 1, 2023, to December 31, 2023, to determine if there's a statistically significant difference in their average daily stock prices and return. This allows us to test if there’s a significant difference in their stock prices and return over the entire year.

Hypothesis:

Null Hypothesis (H₀): There is no significant difference between the average daily stock returns of Apple and Microsoft over the year.

Alternative Hypothesis (): There is a significant difference between the average daily stock returns of Apple and Microsoft over the year.

Set the Null and Alternative Hypothesis mathematically

Collect Stock Data using “STOCKHISTORY” function:

Apple’s stock prices (AAPL):

=STOCKHISTORY("AAPL", "2023/01/01", "2023/12/31",0,2,0,1)

This will give you Apple’s daily closing stock prices from January 1, 2023, to December 31, 2023.

Microsoft’s stock prices (MSFT):

=STOCKHISTORY("MSFT", "2023/01/01", "2023/12/31",0,2,0,1)

This will give you Microsoft’s daily closing stock prices for the same period.

Calculate the Average Stock Prices and Average Daily Return: You can now calculate the average stock prices and daily return for both companies over the selected 12-month period.

Calculate the average stock price of Apple:
Calculate the average stock price of Microsoft:
Calculate the average daily return of Apple:
Calculate the average daily return of Microsoft:

Set the Significance Level: Choose a significance level (α = 0.05), meaning you accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).

Run a t-Test to Compare the Stock Prices: Now, perform a t-Test in Excel to compare the average stock return prices of the two companies.

Interpret the Results: The T.TEST function will return a p-value:

If the p-value ≤ 0.05, you reject the null hypothesis and conclude that there is a significant difference between the average stock prices of Apple and Microsoft.
If the p-value > 0.05, you fail to reject the null hypothesis, meaning there is no statistically significant difference between their stock prices.

Analyzing the Results:

p-value from T.TEST:

Decision based on hypothesis testing:

Would you reject or fail to reject the null hypothesis?

Interpretation:

Is there a significant difference in the average stock prices and returns of Apple and Microsoft over the last year?

Attach the Excel Output Here:

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