Question

Suppose the caffeine amount for a standard 12 -ounce, regular milk latte made at Starbucks follows a normal distribution, with a mean of 64mg and a standard deviation of 1.5mg of caffeine. Suppose the amount of caffeine in a standard 12-ounce, regular milk latte made at Espresso Royale follows a normal distribution, with a mean of 69mg and a standard deviation of 2mg of caffeine. A student receives a standard 12-ounce, regular milk latte from a friend delivered in a personal thermos from one of these two vendors. The student is curious from which vendor the latte came, and views the decision-making process in terms of testing the following hypotheses:

H0 : the latte is from Starbucks versus
Ha : the latte is from Espresso Royale

The student decides to measure the amount of caffeine in the drink and if it is 66mg or higher, the student will conclude the latte is from Espresso Royale.
a. Determine the significance level for this test.

Answer 1

The significance level for this test is 0.05 or 5%.

Step-by-step explanation:

To determine the significance level for this test, we need to calculate the critical value associated with the desired confidence level. In this case, the student has chosen a significance level of 0.05, which corresponds to a common confidence level of 95%.

The critical value for a one-tailed test at a significance level of 0.05 can be found using a z-table or a calculator. For this test, the critical value is approximately 1.645. Therefore, the significance level for this test is 0.05 or 5%.

This distribution will allow you to calculate probabilities such as the probability of exactly

k refrigerators having defective compressors in a sample of size 8, or the cumulative probability up to

k, etc. If you have a specific question or calculation you'd like to perform, feel free to ask!