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:

Capital Structure

The mix of different forms of funds used by a company to finance its overall operations and growth, including debt, equity, and hybrid instruments.

Equity Financing

The process of raising capital through the sale of shares in a company to investors.

Du Pont Identity

A formula that breaks down Return on Equity (ROE) into three component parts: profit margin, asset turnover, and financial leverage, to analyze a company’s financial performance.

Profit Margin

A fiscal indicator calculating the proportion of income left once total costs are subtracted from revenues.