Nutritional information provided by Kentucky Fried Chicken (KFC) claims that each small bag of potato wedges contains 4.8 ounces of food and 280 calories. A sample of ten orders from KFC restaurants in New York and New Jersey averaged 358 calories. Assume that the sample is approximately normally distributed. (a) If the sample deviation was s = 54 calories, is there sufficient evidence to indicate that the average
The Correct Answer and Explanation is :
To determine whether there is sufficient evidence to conclude that the average calorie content of KFC potato wedges differs from the claimed 280 calories, we perform a hypothesis test.
Step 1: Define Hypotheses
- Null Hypothesis ((H_0)): The average calorie content is 280.
[
H_0: \mu = 280
] - Alternative Hypothesis ((H_a)): The average calorie content is different from 280.
[
H_a: \mu \neq 280
]
Step 2: Given Data
- Sample size ((n)) = 10
- Sample mean ((\bar{x})) = 358
- Sample standard deviation ((s)) = 54
- Population mean ((\mu_0)) = 280
- Significance level ((\alpha)) = 0.05
Step 3: Compute Test Statistic
We use the t-test for a single mean:
[
t = \frac{\bar{x} – \mu_0}{s / \sqrt{n}}
]
[
t = \frac{358 – 280}{54 / \sqrt{10}}
]
[
t = \frac{78}{17.08} \approx 4.57
]
Step 4: Find the Critical Value
For a two-tailed test at (\alpha = 0.05) with (df = 10 – 1 = 9), the critical t-value from the t-table is approximately ( \pm 2.262 ).
Step 5: Decision Rule
Since (t = 4.57) is greater than (2.262), we reject the null hypothesis.
Step 6: Conclusion
There is sufficient evidence to conclude that the average calorie content of KFC potato wedges is significantly different from the claimed 280 calories. The test result suggests that KFC’s reported calorie content may not accurately reflect the actual calorie count. Further investigation and larger sample sizes might be necessary to confirm these findings.