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business analyst wants to determine if the prices of goods at a supermarket have changed gnificantly since the new owner of the company took over. She looks at the prices of ten ms before the new owner took over compared to after the new owner started. tem Before Price After Price Difference (After-Before)

business analyst wants to determine if the prices of goods at a supermarket have changed gnificantly since the new owner of the company took over. She looks at the prices of ten ms before the new owner took over compared to after the new owner started. tem Before Price After Price Difference (After-Before)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Title: Analysis of Price Changes in Supermarket Goods** A business analyst aims to determine whether the prices of goods at a supermarket have changed significantly since a new owner took over. The table below presents the prices of ten items before and after the change in ownership. The analysis will help assess the price variations. | Item | Before Price | After Price | Difference (After – Before) | |------|--------------|-------------|-----------------------------| | 1 | $2.50 | $2.80 | $0.30 | | 2 | $3.45 | $3.14 | -$0.31 | | 3 | $6.75 | $7.01 | $0.26 | | 4 | $3.50 | $3.54 | $0.04 | | 5 | $2.89 | $2.95 | $0.06 | | 6 | $3.36 | $3.70 | $0.14 | | 7 | $7.12 | $7.03 | -$0.09 | | 8 | $8.90 | $8.88 | -$0.02 | | 9 | $5.24 | $5.20 | -$0.04 | | 10 | $4.60 | $4.67 | $0.07 | **Summary:** The table illustrates the price differences for each item, calculated by subtracting the "Before Price" from the "After Price." Positive values indicate an increase in price, while negative values indicate a decrease. **Conclusion:** Based on the data in the table and using a significance level of 0.05, the correct \( P \)-value and conclusion regarding whether there is a statistically significant change in prices should be determined through appropriate statistical analysis.
Transcribed Image Text:**Title: Analysis of Price Changes in Supermarket Goods** A business analyst aims to determine whether the prices of goods at a supermarket have changed significantly since a new owner took over. The table below presents the prices of ten items before and after the change in ownership. The analysis will help assess the price variations. | Item | Before Price | After Price | Difference (After – Before) | |------|--------------|-------------|-----------------------------| | 1 | $2.50 | $2.80 | $0.30 | | 2 | $3.45 | $3.14 | -$0.31 | | 3 | $6.75 | $7.01 | $0.26 | | 4 | $3.50 | $3.54 | $0.04 | | 5 | $2.89 | $2.95 | $0.06 | | 6 | $3.36 | $3.70 | $0.14 | | 7 | $7.12 | $7.03 | -$0.09 | | 8 | $8.90 | $8.88 | -$0.02 | | 9 | $5.24 | $5.20 | -$0.04 | | 10 | $4.60 | $4.67 | $0.07 | **Summary:** The table illustrates the price differences for each item, calculated by subtracting the "Before Price" from the "After Price." Positive values indicate an increase in price, while negative values indicate a decrease. **Conclusion:** Based on the data in the table and using a significance level of 0.05, the correct \( P \)-value and conclusion regarding whether there is a statistically significant change in prices should be determined through appropriate statistical analysis.
### Table Data The table presents price data comparisons: | # | Price 1 | Price 2 | Difference | |----|---------|---------|------------| | 5 | $2.89 | $2.95 | $0.06 | | 6 | $3.56 | $3.70 | $0.14 | | 7 | $7.12 | $7.03 | −$0.09 | | 8 | $8.90 | $8.88 | −$0.02 | | 9 | $5.24 | $5.20 | −$0.04 | | 10 | $4.60 | $4.67 | $0.07 | ### Statistical Analysis The question provided is: "Based on the data in the table and using a significance level of 0.05, what is the correct \( P \)-value and conclusion?" ### Options for Conclusion: 1. With a \( t \) statistic of 1.4789 and \( P \)-value of 0.173292, reject the null hypothesis that prices have not changed. 2. With a \( t \) statistic of 1.4789 and \( P \)-value of 0.173292, fail to reject the null hypothesis that prices have not changed. 3. With a \( t \) statistic of 0.7394 and \( P \)-value of 0.478505, reject the null hypothesis that prices have not changed. 4. With a \( t \) statistic of 0.7394 and \( P \)-value of 0.478505, fail to reject the null hypothesis that prices have not changed. ### Analysis Summary To determine the correct conclusion, compare the \( P \)-values with the significance level (0.05). If the \( P \)-value is less than 0.05, reject the null hypothesis. If it is greater, fail to reject the null hypothesis. Options 2 and 4, which fail to reject the null hypothesis, align with both \( P \)-values being greater than 0.05.
Transcribed Image Text:### Table Data The table presents price data comparisons: | # | Price 1 | Price 2 | Difference | |----|---------|---------|------------| | 5 | $2.89 | $2.95 | $0.06 | | 6 | $3.56 | $3.70 | $0.14 | | 7 | $7.12 | $7.03 | −$0.09 | | 8 | $8.90 | $8.88 | −$0.02 | | 9 | $5.24 | $5.20 | −$0.04 | | 10 | $4.60 | $4.67 | $0.07 | ### Statistical Analysis The question provided is: "Based on the data in the table and using a significance level of 0.05, what is the correct \( P \)-value and conclusion?" ### Options for Conclusion: 1. With a \( t \) statistic of 1.4789 and \( P \)-value of 0.173292, reject the null hypothesis that prices have not changed. 2. With a \( t \) statistic of 1.4789 and \( P \)-value of 0.173292, fail to reject the null hypothesis that prices have not changed. 3. With a \( t \) statistic of 0.7394 and \( P \)-value of 0.478505, reject the null hypothesis that prices have not changed. 4. With a \( t \) statistic of 0.7394 and \( P \)-value of 0.478505, fail to reject the null hypothesis that prices have not changed. ### Analysis Summary To determine the correct conclusion, compare the \( P \)-values with the significance level (0.05). If the \( P \)-value is less than 0.05, reject the null hypothesis. If it is greater, fail to reject the null hypothesis. Options 2 and 4, which fail to reject the null hypothesis, align with both \( P \)-values being greater than 0.05.
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