Problem Description
The statistical analysis assignment is to analyze Chips Ahoy, a beloved brand that has been satisfying sweet cravings since 1963, is renowned for its crunchy cookies packed with milk chocolate chips. However, despite its popularity, some customers have expressed concerns about the quantity of chips in each cookie compared to other brands on the market. To address this, our study aims to investigate whether Chips Ahoy cookies contain more chips per cookie compared to another brand, PC cookies. We meticulously counted and recorded the number of chips in ten distinct Chips Ahoy cookies and ten PC cookies to test this hypothesis.
Statistical Test
To determine if Chips Ahoy cookies indeed contain more chips per cookie than PC cookies, we conducted an independent student t-test. Our hypothesis and decision rule were as follows:
- Null Hypothesis: Chips Ahoy cookies have more chips per cookie than PC cookies.
- Alternative Hypothesis: Chips Ahoy cookies have fewer chips per cookie than PC cookies.
- Decision Rule: We would reject the null hypothesis if the test statistic is less than the critical value or if the p-value is less than 0.05.
For detailed calculations, please refer to the attached hand calculation and Excel file.
Results
After conducting the t-test, we found that the null hypothesis cannot be rejected. The test statistic (-0.818) is greater than the critical value (-1.7341), indicating that Chips Ahoy cookies do not contain significantly fewer chips per cookie than PC cookies.
Conclusion
Our analysis using an independent t-test suggests that Chips Ahoy cookies, on average, have more chips per cookie than PC cookies. The t-statistic was -0.818, with a corresponding p-value of 0.212.
Manual Calculation
