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Vanyuwa [196]
3 years ago
10

In a survey from 1998, 449 teenagers were surveyed about the music that they listen to. Of these teenagers, 129 of them said tha

t their favorite genre of music is hip-hop. In a similar survey from 2008, 176 of 509 teenagers surveyed said that their favorite genre is hip-hop. Use a two-proportion hypothesis test to determine whether the proportion of teenagers whose favorite genre of music is hip-hop has changed from 1998 to 2008. Assume that the samples are random and independent. Use α=0.01. Let the sample from 1998 correspond to sample 1 and the other to sample 2. (a) Which answer choice shows the correct null and alternative hypotheses for this test? Select the correct answer below: H0:p1=p2; Ha:p1p2, which is a right-tailed test. H0:p1=p2; Ha:p1≠p2, which is a two-tailed test.
Mathematics
1 answer:
marshall27 [118]3 years ago
6 0

Answer:

H0:p1=p2; Ha:p1≠p2, which is a two-tailed test.

Step-by-step explanation:

We formulate our hypotheses as

H0:p1=p2; Ha:p1≠p2, which is a two-tailed test.

Supposing the probability or proportion of the first survey is equal to the probability or proportion of the second survey. This will be the null hypothesis and the alternative hypotheses would be that these two proportions or probabilities are unequal.

This is a two tailed test.

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Solving a trigonometric equation involving an angle multiplied by a constant
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In these questions, we need to follow the steps:

1 - solve for the trigonometric function

2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.

3 - Complete these angles with the complete round repetition, by adding

2k\pi,k\in\Z

4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.

1 - To solve, we just use algebraic operations:

\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}

2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:

The value for the angle that give positive

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is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of

-\frac{\sqrt[]{3}}{3}

Are:

\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}

3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:

\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}

Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:

\theta=\frac{5\pi}{6}+k\pi,k\in\Z

4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:

\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}

So, the solutions are:

x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z

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