The Scores on a Standardized Test Are Reported by the Testing

question 19

Essay

The scores on a standardized test are reported by the testing agency to have a mean of 75.
Based on his personal observations, a school guidance counselor believes the mean score is much higher. He collects the following scores from a sample of 50 randomly chosen students who took the test.

$$\begin{array}{l}\begin{array} { l l l l l l l l l l } 39 & 48 & 55 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 99\end{array}\\\\\text { Find and interpret the } p \text {-value for the test of } H _ { 0 } : \mu = 75 \text { against } H _ { \mathrm { a } } : \mu > 75 \text {. }\end{array}$$

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Definitions:

Spread

The difference between two prices or rates, such as the bid and ask price of a stock, or the interest rates of two different investments.

Yield to Maturity

The total return anticipated on a bond if the bond is held until it matures, including both interest payments and capital gains.

Bond Indenture

A legal and binding contract between a bond issuer and the bondholders, specifying the terms of the bond such as the interest rate, maturity date, and other conditions.

Flotation Costs

Expenses associated with issuing new stocks or bonds, including fees for underwriting services, legal counsel, and registration.