Question

2. A coffee shop prides itself on serving 12-ounce cups of its signature espresso blend. The coffee dispensing machine is calibrated to produce cups with a mean volume of 12 ounces and a standard deviation of 0.5 ounces, following a normal distribution. To ensure consistency, the shop manager randomly selects nine cups of espresso and measures their volumes. a) Find the margin of error for a 90% confidence interval for the mean volume. b) Suppose the shop manager wishes to reduce the margin of error to 0.2 ounces. What is the minimum sample size that would be required to perform the same test with 90% confidence? Discuss how and why your answer changed compared to that in part a). c) Suppose the shop manager wishes to reduce the margin of error to 0.2 ounces and also increase the confidence to 95%. What is the minimum sample size that would be required to perform the same test with 95% confidence? Discuss how and why your answer changed compared to that in part b).

Name: 2 a coffee shop prides itself on serving 12 ounce cups of its signature espresso blend the coffee dispensing machine is calibrated to produce cups with a mean volume of 12 ounces and a stand 46337
Uploaded: 2023-05-14T00:15:53-08:00
Duration: 2 min 53 s
Channel: Kari Hasz
Description: 2 a coffee shop prides itself on serving 12 ounce cups of its signature espresso blend the coffee dispensing machine is calibrated to produce cups with a mean volume of 12 ounces and a stand 46337

          2. A coffee shop prides itself on serving 12-ounce cups of its signature espresso blend. The coffee dispensing machine is calibrated to produce cups with a mean volume of 12 ounces and a standard deviation of 0.5 ounces, following a normal distribution. To ensure consistency, the shop manager randomly selects nine cups of espresso and measures their volumes.
a) Find the margin of error for a 90% confidence interval for the mean volume.
b) Suppose the shop manager wishes to reduce the margin of error to 0.2 ounces. What is the minimum sample size that would be required to perform the same test with 90% confidence? Discuss how and why your answer changed compared to that in part a).
c) Suppose the shop manager wishes to reduce the margin of error to 0.2 ounces and also increase the confidence to 95%. What is the minimum sample size that would be required to perform the same test with 95% confidence? Discuss how and why your answer changed compared to that in part b).

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