Exercise \(\PageIndex{5}\)
The mean price of midsized cars in a region is $32,000. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.
 Answer

Type I: The mean price of midsized cars is $32,000, but we conclude that it is not $32,000.
Type II: The mean price of midsized cars is not $32,000, but we conclude that it is $32,000.
Exercise \(\PageIndex{6}\)
A sleeping bag is tested to withstand temperatures of –15 °F. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.
Exercise \(\PageIndex{7}\)
For Exercise 9.12, what are \(\alpha\) and \(\beta\) in words?
 Answer

\(\alpha =\) the probability that you think the bag cannot withstand 15 degrees F, when in fact it can
\(\beta =\) the probability that you think the bag can withstand 15 degrees F, when in fact it cannot
Exercise \(\PageIndex{8}\)
In words, describe \(1  \beta\) For Exercise \(\PageIndex{}\)
Exercise \(\PageIndex{9}\)
A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, \(H_{0}\), is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences.
 Answer

Type I: The procedure will go well, but the doctors think it will not.
Type II: The procedure will not go well, but the doctors think it will.
Exercise \(\PageIndex{10}\)
A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, \(H_{0}\), is: the surgical procedure will go well. Which is the error with the greater consequence?
Exercise \(\PageIndex{11}\)
The power of a test is 0.981. What is the probability of a Type II error?
 Answer

0.019
Exercise \(\PageIndex{12}\)
A group of divers is exploring an old sunken ship. Suppose the null hypothesis, \(H_{0}\), is: the sunken ship does not contain buried treasure. State the Type I and Type II errors in complete sentences.
Exercise \(\PageIndex{13}\)
A microbiologist is testing a water sample for Ecoli. Suppose the null hypothesis, \(H_{0}\), is: the sample does not contain Ecoli. The probability that the sample does not contain Ecoli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain Ecoli, but the microbiologist thinks it does not is 0.002. What is the power of this test?
 Answer

0.998
Exercise \(\PageIndex{14}\)
A microbiologist is testing a water sample for Ecoli. Suppose the null hypothesis, \(H_{0}\), is: the sample contains Ecoli. Which is the error with the greater consequence?