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# 36 you may assume that the data is drawn from a normal population.

9.36 <— you may assume that the data is drawn from a normal population.

1,Wine-pouring vending machines, previously available in Europe and international airports, have become popular in the last few years in the United States. They are even approved to dispense wine in some Wal-Mart stores. The available pouring options are a 5-ounce glass, a 2.5-ounce half-glass, and a 1-ounce taste. When the machine is in statistical control (see Exercise 7.42), the amount dispensed for a full glass is 5.1 ounces. Four observations are taken each day, to plot a daily mean over time on a control chart to check for irregularities. The most recent day’s observations were 5.05, 5.15, 4.95, and 5.11. Could the difference between the sample mean and the target value be due to random variation, or can you conclude that the true mean is now different from 5.1? Answer by showing the five steps of a significance test, making a decision using a 0.05 significance level

2,also assume that the machine dispenses wine in a random manner

9.46

refer to the previous exercise. when we test H0: M=0 against Ha: M>0, we get a p-value of 0.02

- what would the decision be for a significance level of 0.05? interpret in context.
- if the decision in part a is in error, what type of error is it?
- suppose the significance level were instead 0.01. what decision would you make, and if it is in error, what type of error is it?

9.50

Detecting prostate cancer:Refer to the previous exercise about medical diagnoses. A

New York Times article (February 17, 1999) about the PSA blood test

for detecting prostate cancer stated: “The test fails to detect prostate cancer in 1 in 4 men who have the disease.”

a. For the PSA test, explain what a Type I error is, and explain the consequence to a

man of this type of error.

b. For the PSA test, what is a Type II error? What is the consequence to a man of this

type of error?

c. To which type of error does the probability of 1 in 4 refer?

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- Attachment 2