Which Is Cheaper: Eating In Or Dining Out The Mean Cost Of A

Question

which Is Cheapereating In Or Dining Outthe Mean Cost Of A Flank S Analyze whether eating in or dining out is more cost-effective by comparing the average costs of comparable meals. The mean cost of a flank steak, broccoli, and rice bought at the grocery store is $13.04. A sample of 100 neighborhood restaurants showed an average price of $12.75 with a standard deviation of $2. Conduct a hypothesis test at a 95% confidence level to determine if there is evidence that the average restaurant meal costs less than preparing a comparable meal at home. Interpret the results and explain your conclusions. Additionally, interpret the statistical significance and practical implications of the findings, considering factors such as variance and sample size.

Dr. Jack HW Helper · Accepted Answer

Introduction The cost comparison between eating at home and dining out has been a subject of economic and consumer interest. This analysis aims to determine whether dining out offers a cheaper alternative by statistically examining the average costs involved. Specifically, this study compares the mean cost of preparing a meal at home with that of purchasing a similar meal at a restaurant, using sample data and hypothesis testing methods. Data and Methodology The known mean cost of a home-cooked meal consisting of flank steak, broccoli, and rice is $13.04. To assess restaurant prices, a sample of 100 restaurants was analyzed, revealing an average meal cost of $12.75 with a standard deviation of $2. The research question hinges on whether the mean restaurant meal is significantly less expensive than the home meal. The hypothesis test formulated is as follows: Null hypothesis (H₀): μ = $13.04 (The average restaurant meal cost is equal to the cost of preparing the meal at home.) Alternative hypothesis (H₁): μ Given the large sample size (n=100), a z-test is appropriate for this analysis. The test statistic is calculated using the sample mean, population mean, standard deviation, and sample size. Results Calculating the z-statistic: z = (x̄ - μ₀) / (σ / √n) = (12.75 - 13.04) / (2 / √100) = (-0.29) / (0.2) = -1.45 Looking up the p-value associated with z = -1.45 in the standard normal distribution yields p ≈ 0.0735 (one-tailed test). Since the significance level (α) is 0.05, and the p-value (0.0735) exceeds α, we fail to reject the null hypothesis. Discussion and Conclusion The statistical analysis indicates that there is insufficient evidence at the 95% confidence level to conclude that dining out is cheaper than preparing a meal at home. The observed mean restaurant meal cost is slightly lower than the cost of a home-cooked meal, but this difference is not statistically significant at the conventional level. Practically, this suggests that while restaurants may sometime

Which Is Cheaper: Eating In Or Dining Out The Mean Cost Of A ✓ Solved

which Is Cheapereating In Or Dining Outthe Mean Cost Of A Flank S

Sample Paper For Above instruction

Introduction

Data and Methodology

Results

Discussion and Conclusion

Limitations and Further Research

References