The data suggest that the true proportion of Teen Court individuals who recidivate during the specified follow-up period differs from the proportion of Department of Juvenile Services individuals

Step-by-step explanation:

Step(i):-

Given first sample size (n₁ ) = 57

Of the 57 Teen Court individuals, 18 subsequently recidivated during the 18-month follow-up period

First sample proportion

$p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{18}{57} =0.3157$

Second sample proportion

$p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{11}{54} =0.2037$

Null Hypothesis : p₁⁻ = p₂⁻

Alternative Hypothesis : p₁⁻ ≠ p₂⁻

Step(ii):-

Test statistic

$Z = \frac{p_{1} ^{-} -p^{-} _{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }$

where

$P = \frac{n_{1}p^{-} _{1} +n_{2} p^{-} _{2} }{n_{1} +n_{2} }$

$P = \frac{57 X0.3157+0.2037X54}{54+57} = 0.2612$

Q = 1 - P = 1 - 0.2612 = 0.7387

$Z = \frac{0.3157-0.2037}{\sqrt{0.2612 X0.7387 (\frac{1}{57} +\frac{1}{54} )} }$

Z = 1.4017

Level of significance ∝ =0.05

The tabulated value Z₀.₀₅ = 1.96

Z-statistic = 1.4017 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

The data suggest that the true proportion of Teen Court individuals who recidivate during the specified follow-up period differs from the proportion of Department of Juvenile Services individuals

7 0

3 years ago

If sin 22.6°=5/13, what is cos 67.4° ?

lara [203]

The value of cos 67.4° is 5/13.

According to trigonometric identities used in mathematics, sin of an angle is equal to cos of 90 - the given angle. Mathematically, this means that, suppose we have an angle x, then-

sin(90 - x) = cos x

Here, we are given that sin 22.6° = 5/13. As we can observe that (90 - 67.4) is equal to 22.6, and we need to find the value of cos 67.4° only. Thus we can write the given equation as follows-

sin22.6° = sin(90 - 67.4°)

= cos 67.4°

Thus, sin 22.6° = cos 67.4°

Hence, cos 67.4° = 5/13

Thus, the value of cos 67.4° comes out to be 5/13.

Learn more about trigonometric identities here-

brainly.com/question/7331447

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3 0

1 year ago

Below is a blue rectangle with a width of 27.5 cm and a length of 33 cm. An orange rectangle with a width of 15 cm and a length

Montano1993 [528]

Orange: 300
blue: 907.5

explanation: area is length time width. take those values and multiply

5 0

3 years ago

What is the value for x? 69 (5x + 2) Enter your answer in the box (9y-3)

Leviafan [203]

Answer:

$5x + 2 \\ x = 5 - 2 \\ x = 3 \\ \\ 9y - 3 \\ y = 9 + 3 \\ y = 12$

4 0

3 years ago