Explain Type I and Type II Errors
-A Local Tennis $\bar { x } = 49 \mathrm { psi } , \mathrm { s } = 4.0 \mathrm { psi }$

question 48

Multiple Choice

Explain Type I and Type II Errors
-A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 16 new rackets at 50 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics: $\bar { x } = 49 \mathrm { psi } , \mathrm { s } = 4.0 \mathrm { psi }$ . In order to conduct the test, the customer selected a significance level of $\alpha = .01$ . Interpret this value.

• A) The probability of concluding that the true mean is less than 50 psi when in fact it is equal to 50 psi is only \(.01\).
• B) The smallest value of \(\alpha\) that you can use and still reject \(\mathrm { H } _ { 0 }\) is \(0.01\).
• C) The probability of making a Type II error is \(0.99\).
• D) There is a \(1 \%\) chance that the sample will be biased.

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Definitions:

Out Of Control Signals

Indicators within a process control or statistical control chart that highlight when a process is deviating from its stable state or specified limits.

Sampling Distribution

The probability distribution of a given statistic based on a random sample, used to make inferences about the population.

Common Cause Variation

The variation in a process that is random and inherent to the process itself, as opposed to being caused by identifiable factors.

Conjugate Acid

The species formed when a base gains a proton (H+), effectively showing the protonated form of the base.