Using the z-distribution, it is found that since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.

At the null hypothesis, it is tested if the mean length of jail time is still of 2.5 years, that is:

$H_0: \mu = 2.5$

At the alternative hypothesis, it is tested if it has increased, that is:

$H_1: \mu > 2.5$

We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.
$\mu$ is the value tested at the null hypothesis.
$\sigma$ is the standard deviation of the sample.
n is the sample size.

For this problem, the values of the parameters are: $\overline{x} = 3, \mu = 2.5, \sigma = 1.5, n = 26$

Hence, the value of the test statistic is:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{3 - 2.5}{\frac{1.5}{\sqrt{26}}}$

$z = 1.7$

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05, is of $z^{\ast} = 1.645$

Since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.

A similar problem is given at brainly.com/question/24166849

5 0

2 years ago

2|4x-1|=38 I need to solve this

umka21 [38]

First you have to have the absolute value isolated so the 2 has to be divided. Then set up the two cases and solve.

5 0

3 years ago

Find the area of the following polygon:

Masja [62]

Given:

ABCD is a quadrilateral

AC = 12, DE = 4 and FB = 5

To find:

The area of the polygon.

Solution:

AC bisects the quadrilateral into two triangles.

Area of triangle:

$$A=\frac{1}{2}\times\text{base}\times\text{height}$

Area of triangle DAC:

$$A=\frac{1}{2}\times AC \times DE$

$$A=\frac{1}{2}\times 12 \times 4$

$A=24$

Area of triangle DAC = 24 square units.

Area of triangle BAC:

$$A=\frac{1}{2}\times AC \times FB$

$$A=\frac{1}{2}\times 12 \times 5$

$A=30$

Area of triangle BAC = 30 square units.

Area of polygon = Area of triangle DAC + Area of triangle BAC

= 24 square units + 30 square units

= 54 square units

The area of the polygon is 54 square units.

3 0

3 years ago

Pleas help me out here.

Amiraneli [1.4K]

Answer:

A and E

Step-by-step explanation:

The given problem shows a graph of a vertical line with an undefined slope, in which its equation is x = 3 (which matches Option A).

It is not considered a function because it has the same input for every given output. This means that regardless of its y-coordinate, its corresponding x-coordinate will always be x = 3.

The Vertical Line Test allows us to know whether or not a graph is actually a function. Remember that a function can only take on one output for each input. We cannot plug in a value and produce two output values. Since the graph represents a vertical line, it automatically fails the vertical line test. Therefore, it is not a function.

Because it is not a function, Options B, C, and D are invalid answers.

Hence, the correct answers are Options A and E.

4 0

2 years ago