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The number of cups of coffee served at a local Tim Horton’s during the morning rush...

  1. 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. Based on sales a day is described as SLOW if less than 200 cups are served, AVERAGE 200- 249 cups are sold, and BUSY if over 250 cups are sold during the day. A random sample of five days was taken and the sales figures observed. The sample mean is 208 cups and the sample standard deviation is 25.5734.

  1. (6) Construct a 99% confidence interval for the population average sales for this period.
  2. (2) 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.
  3. (6) Management is concerned that the average is falling below the national average of 210 cups per day. Test this hypothesis using alpha = 0.05.
  4. (1) What assumption must hold to allow you to construct the confidence interval and test the hypothesis in this case?
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Answer #1

Construct a 99% confidence interval for the population average sales for this period.

We are given sample mean = ji= 208 sample standard deviation = 0 = 25.5734 n = 5 a/2 = (1-0.99)/2= 0.005 df = n - 1 = 4 Using

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.

The confidence interval extends from 155 cups to 260 cups. Hence if would fall in a slow to an average type of day

.Management is concerned that the average is falling below the national average of 210 cups per day. Test this hypothesis using alpha = 0.05.

The provided sample mean is X = 208 and the sample standard deviation is s = 25.5734, and the sample size is n = 5. (1) Null

Hence we can conclude that there is not enough evidence to conclude that the average is less than the national average of 210

What assumption must hold to allow you to construct the confidence interval and test the hypothesis in this case?

THe sample must be taken randomly.
Each sample must be independent

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