Question: Nutritional information provided by 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. If the sample standard deviation was s=54, is there sufficient evidence to indicate that the average number of calories in small bags of KFC potato wedges is greater than advertised? Test at 5% significance level.

Null hypothesis:

Alternative hypothesis:

The value of the test statistic:

The critical value of the test:

Conclusion:

b. Using the above information, construct a 95% confidence interval for the true mean number of calories in small bags of KFC potato wedges.