1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dmitriy555 [2]
3 years ago
8

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

the arrests were not prosecuted. Using this information, one officer wants to test the claim that the number of arrests that are never prosecuted is under what the chief stated. Is there enough evidence at the 0.02 level to support the officer's claim?
Mathematics
1 answer:
Elis [28]3 years ago
3 0

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.  

You might be interested in
Help With This Question ASAP!!!​
ch4aika [34]

Answer:

43.25-7-(t*1.15)

Step-by-step explanation:

because oBaMa

8 0
3 years ago
Read 2 more answers
Which equation would give the graph below? (photo)
emmasim [6.3K]

Answer:

C

Step-by-step explanation:

Y= 4^2 - 5 x 4 + 4 = 0

5 0
3 years ago
I got really confused and I really don’t know what to do and I try to do for myself but I didn’t get it
otez555 [7]

Answer:

The Answer is A. I made a graph and those points are the only ones that made a line.

5 0
3 years ago
What is the yintercept in the equation y=4x-3?
sergejj [24]

Answer:

-3

Step-by-step explanation:

The main formula for slope intercept form is y=mx+b

m=slope

b=y-intercept

3 0
3 years ago
Anna read 1/8 a book in 1/2 an hour. How much can she read in an hour?
Travka [436]

Answer:

2/8 of a book in an hour

Step-by-step explanation:

1/2 an hour times 2 is 1 ( an hour)

1/8 times 2 is 2/8

she can read 2/8 of a book in an hour

8 0
2 years ago
Read 2 more answers
Other questions:
  • Help please ASAP!!!! I NEED CORRECT ANSWERS ONLY FOR BRAINLIEST
    9·1 answer
  • How do you do exterior angles of triangles
    10·2 answers
  • Please help! z &gt; 34. Which of the following statements is the best way to describe the value of z?
    6·2 answers
  • The measure of &lt;1 = 20x + 21 and the measure of &lt;2 = 30x - 29.
    7·1 answer
  • Solve for x:
    15·1 answer
  • Which expression is equivalent to 9c + 7c
    12·1 answer
  • The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $5.50 and
    7·1 answer
  • Sue bought a bunch of snacks that each cost $2.50. Let y represent the total cost and x represent the number of snacks she bough
    7·1 answer
  • Judah's family wants to ride the bumper boats at a water park. There are 4 children (c) and 2 adults 9 (a) in Judah's family. Th
    13·2 answers
  • 7y2 - 7y+ 4<br> -(-3y2 + 7y + 7)<br> (Simplify your answer.)
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!