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Answer:
The length of the shortest side of the triangle is 10 units.
Step-by-step explanation:
Let <em>a</em> be the shortest side of the isosceles triangle and <em>b</em> be the two congruent sides.
The congruent sides <em>b</em> are each one unit longer than the shortest side. Hence:
The perimeter of the isosceles triangle is given by:
This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be <em>s</em>. Hence:
The perimeter of the square is:
Since the two perimeters are equivalent:
Substitute for <em>b: </em>
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Solve for <em>a</em>. Distribute:
Simplify:
Hence:
The length of the shortest side of the triangle is 10 units.
The probability of making a type II error is given by one minus the power of the hypothesis test.
In general for the alternative hypothesis ,
The power of a hypothesis test is given by:
The probability of <span>making a type ii error when μ = 31,000 is given by
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In general for the alternative hypothesis ,
The power of a hypothesis test is given by:
The probability of <span>making a type ii error when μ = 31,000 is given by