Determine whether the system of equations has no solution, one solution, or infinitely many solutions

A local police chief claims that 31% of all drug-related arrests are never prosecuted. A sample of 500 arrests shows that 27% of

Elis [28]

Answer:

$z=\frac{0.27 -0.31}{\sqrt{\frac{0.31(1-0.31)}{500}}}=-1.933$

$p_v =P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.02$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.

Step-by-step explanation:

1) Data given and notation

n=500 represent the random sample taken

X represent the number of arrests that were not prosecuted.

$\hat p=0.27$ estimated proportion of arrests that were not prosecuted

$p_o=0.31$ is the value that we want to test

$\alpha=0.02$ represent the significance level

Confidence=98% or 0.98

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.31.:

Null hypothesis: $p\geq 0.31$

Alternative hypothesis: $p < 0.31$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.27 -0.31}{\sqrt{\frac{0.31(1-0.31)}{500}}}=-1.933$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.02$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.02$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.

3 0

3 years ago

Consider the following data set: 0, 10, 12, 3, 13, 7, 2, 5 Find the upper quartile.

weeeeeb [17]

Answer:

11

Step-by-step explanation:

The upper quartile Q3 is the median of the upper half of the data.

6 0

2 years ago

Find the area of a regular triangle with side length of 15.5 inches

Ganezh [65]

Answer:

Brainliest pls

Step-by-step explanation:

A≈104.03in²

5 0

2 years ago

Which function is graphed?

Hitman42 [59]

Answer: D

x < 1 is parabol curve

x ≥ 1 is a line

5 0

3 years ago

At Acme Inc., there are 3 more than twice as many salespeople as inventors. If the whole company has 27 employees,

Olenka [21]

Answer:

There are 8 inventors.

Step-by-step explanation:

Let 's' be the salesperson

Let 'i' be the inventors

Given that there are 3 more than twice as many salespeople as inventors.

i.e s = 3+2i

Also given that the whole company has 27 employees.

i.e.

s + i = 27

substituting s = 3+2i

3 + 2i + i= 27

3 + 3i = 27

3i = 27 - 3

3i = 24

divide both sides by 3

i = 8

Thus, there are 8 inventors.

VERIFICATION

As the total number of employees is 27.

so the salespeople will be:

s = 3+2i

= 3 + 2(8)

= 3 + 16

= 19

Thus, the total employees are verified as:

s + i = 27

19 + 8 = 27

27 = 27

4 0

2 years ago