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The number of cups of coffee served at a local Tim Horton's during the morning rush hour between 7 and 9 AM is normally distributed. Less than 200 cups served is considered a slow day, 200- 249 an average day, and over 250 a busy day. A random sample of five days was taken and the sales figures observed. The results are as follows:
184 212 194 250 200
a. Calculate the sample average and sample standard deviation for this data.
b. Construct a 99% confidence interval for the population average sales for this period.
c. Based on your confidence interval, can you conclude the type of day that the average sales would be considered as defining - slow, average, or busy? Explain your conclusion.
d. Management is concerned that the average is falling below the national average of 210 cups during this period. Test this hypothesis using alpha = 0.05.
e. What assumptions must hold to allow you to construct the confidence interval and test the hypothesis in this case?
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