Restaurant Hospitality

In 2017, the Restaurant Hospitality website reported that only 11% of surplus food is being recovered in the food service and restaurant sector, leaving approximately 1.5 billion meals per year uneaten. Assume that this is the true population proportion and that you plan to take a sample survey of 525 companies in the food service and restaurant sector to further investigate their behavior. You suspect that restaurants are doing a far better job in recovering surplus food than what has been reported by the website.
Suppose that based on the sample you collected restaurants report an average of 59 surplus meals per day of which an equivalent of 51 meals is thrown away. Respond to the following questions:
a. Set up the research question and hypotheses. – Let’s set up Accounting related question.
b. Calculate the p-value using the “Norm.dist” Excel command.
c. What is your conclusion?

Sample Answer

Statistical Analysis: Surplus Food Recovery in the Restaurant Industry

a. Research Question & Hypotheses

Research Question:

“Do restaurants recover a higher proportion of surplus food than the reported 11%?”

Hypotheses:

- - Null Hypothesis (H₀): p = 0.11 (Restaurants recover 11% of surplus food).
  - Alternative Hypothesis (H₁): p > 0.11 (Restaurants recover >11% of surplus food).

Rationale: The suspicion is that restaurants are doing better than 11%, so this is a right-tailed test.

b. Calculating the p-value (Using Excel’s NORM.DIST)

Given Data:

- Population proportion (p₀): 0.11 (11%).
- Sample size (n): 525 restaurants.
- Sample mean (x̄): 59 surplus meals/day.
- Sample waste (w): 51 meals/day.

Full Answer Section

$= 5959 - 51 = 598 \approx 0.1356 (13.56%)$

Standard Error (SE) Calculation:

$SE = n p ^{0} ( 1 - p ^{0} ) = 5250.11 \times 0.89 \approx 0.0137$

Z-Score Calculation:

$z = SE p ^ - p ^{0} = 0.01370.1356 - 0.11 \approx 1.87$

p-value (Excel Command):

excel

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=NORM.DIST(1.87, TRUE, FALSE) // Returns 0.9693

p-value = 1 – 0.9693 = 0.0307

c. Conclusion

Interpretation:

p-value (0.0307) < α (0.05) → Reject H₀.
Conclusion: There is sufficient evidence at the 5% significance level to conclude that restaurants recover more than 11% of surplus food.

Business Implication:

Restaurants are indeed performing better than reported, but there’s still room for improvement (only 13.56% recovery vs. 88.44% waste).

Recommendation: Investigate best practices among top performers to further increase recovery rates.

Final Answer

p-value = 0.0307
Conclusion: Reject H₀; restaurants recover >11% of surplus food.

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