# Outcomes and the Type I and Type II Errors (Exercises)

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##### Exercise $$\PageIndex{5}$$

The mean price of mid-sized 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 mid-sized cars is$32,000, but we conclude that it is not $32,000. Type II: The mean price of mid-sized 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?

$$\alpha =$$ 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.

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?

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 E-coli. Suppose the null hypothesis, $$H_{0}$$, is: the sample does not contain E-coli. The probability that the sample does not contain E-coli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E-coli, but the microbiologist thinks it does not is 0.002. What is the power of this test?

##### Exercise $$\PageIndex{14}$$
A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, $$H_{0}$$, is: the sample contains E-coli. Which is the error with the greater consequence?