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3 years ago

8

Previous studies on sleep tendencies report that, on average, an adult American will sleep for 6 hours each night with a standar

d deviation of 0.75 hours. You survey a SRS of 100 adult Americans and determine that the mean sleep time is 5 hours. Which Hypothesis Test should be used here

1 answer:

Tom [10]3 years ago

7 0

Answer: One sample z test for means

Step-by-step explanation:

From the information given, the sample size is large. It is greater than 30. Again, the population standard deviation is given. This means that the test statistic would be the z score which is determined by the formula

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

The probability value would be determined from the normal distribution table.

Therefore, the hypothesis test that should be used is

One sample z test for means

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2 years ago

A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u

Kryger [21]

Given: $f(x) = \frac{1}{x-2}$

$g(x) = \frac{2x+1}{x}$

A.)Consider

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$f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}$

$f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}$

$f(\frac{2x+1}{x} )=\frac{x}{1}$

$f(\frac{2x+1}{x} )=1$

Also,

$g(f(x))= g(\frac{1}{x-2} )$

$g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{x }{1}$

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Therefore, both functions are inverses of each other.

B.

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Since, the function $f(g(x))$ is not defined for $x=0$ .

Therefore, the domain is $(-\infty,0)\cup(0,\infty)$

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Since, the function $g(f(x))$ is not defined for $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

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3 years ago

A right triangle has a hypotenuse length of 60, and one side length of 24. Do the side lengths form a Pythagorean triple? Explai

Alexeev081 [22]

You can test this using the equation: a^2 + b^2 = c^2.

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3 years ago