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
spin [16.1K]
3 years ago
14

70% of the U.S. population recycles. According to a green survey of a random sample of 250 college students, 204 said that they

recycled. At alpha = 0.01, is there sufficient evidence to conclude that the proportion of college students who recycle is greater than 70%?
Mathematics
1 answer:
pav-90 [236]3 years ago
3 0

Answer:

z=\frac{0.816 -0.7}{\sqrt{\frac{0.7(1-0.7)}{250}}}=4.002  

p_v =P(z>4.002)=0.0000314  

So the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of people said that they recycled is significantly higher than 0.7 or 70%

Step-by-step explanation:

Data given and notation

n=250 represent the random sample taken

X=204 represent the people said that they recycled

\hat p=\frac{204}{250}=0.816 estimated proportion of people said that they recycled

p_o=0.7 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.7.:  

Null hypothesis:p\leq 0.7  

Alternative hypothesis:p > 0.7  

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.

Calculate the statistic  

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

z=\frac{0.816 -0.7}{\sqrt{\frac{0.7(1-0.7)}{250}}}=4.002  

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=0.01. The next step would be calculate the p value for this test.  

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

p_v =P(z>4.002)=0.0000314  

So the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of people said that they recycled is significantly higher than 0.7 or 70%

You might be interested in
What's the square root of 25 in **simplest radical form**
den301095 [7]

Answer:

5

Step-by-step explanation:

The square Root of 25 in its simplest form means to get the number 25 inside the radical √ as low as possible.

25 is a perfect square, which means that you can simply calculate the square Root of 25 to get the answer. 5 times 5 equals 25. Thus, the square Root of 25 in simplest radical form is:

5

6 0
2 years ago
(x-1)^2+(2-x)^2-3(x-5)*(x-5)
Natali5045456 [20]

Answer:

-x^2+24x-70

Step-by-step explanation:

(x-1)^2+(2-x)^2-3(x-5)*(x-5)\\=> (x - 1)^2 + (2 - x)^2 - 3(x - 5)^2\\=> x^2 - 2x + 1 + 4 - 4x + x^2 - 3(x - 5)^2\\=> x^2 - 2x + 5 - 4x + x^2 - 3(x - 5)^2\\=> x^2 - 6x + 5 + x^2 - 3(x - 5)^2\\=> 2x^2 - 6x+5 - 3(x - 5)^2\\=> 2x^2 - 6x+5 - 3(x^2 - 10x + 25)\\=> 2x^2 - 6x+5  - 3x^2+30x-75\\=> -x^2 - 6x + 5 + 30x - 75\\=> -x^2 + 24x + 5-75\\=> -x^2+24x-70

Formula used =

(a-b)^2 = a^2+ 2ab + b^2

8 0
2 years ago
100 points!!! PLEASE ANSWER IT HOW I HAVE IT IN ORDER!!
Anvisha [2.4K]

Answer: Have a good day. I’m sorry you have to go through this, my head already hurts and I am just lōoking at it.

8 0
2 years ago
Read 2 more answers
Find the values of x and y
zhuklara [117]

You can use a tangent:

tangent=\dfrac{opposite}{adjacent}

We have opposite = 17 and adjacent = x.

\tan30^o=\dfrac{\sqrt3}{3}

substitute:

\dfrac{17}{x}=\dfrac{\sqrt3}{3}       cross multiply

x\sqrt3=(3)(17)     multiply both sides by √3

x(\sqrt3)(\sqrt3)=51\sqrt3

3x=51\sqrt3      divide both sides by 3

x=17\sqrt3

Use the Pythagorean theorem:

y^2=(17\sqrt3)^2+17^2\\\\y^2=289(\sqrt3)^2+289\\\\y^2=289\cdot3+289\\\\y^2=867+289\\\\y^2=1156\to y=\sqrt{1156}\\\\y=34

-------------------------------------------------------------------------------------------------

Other method.

30^o-60^o-90^o triangle.

The sides are in the ratio 1:2:\sqrt3\to17:y:x

Therefore

17:(2\cdot17):(17\sqrt3)\to17:34:17\sqrt3\to x=34,\ y=17\sqrt3

 


4 0
3 years ago
jenna has 4 double fudge brownies to share with 5 people including yourself how can jenna share the brownies equally.
Oliga [24]

Answer:

4÷5=0.8      or    4/5

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Pythagoras' theorem​
    9·2 answers
  • Use the proportion to convert milligrams to grams.
    15·2 answers
  • Gaelle et maeva souhaitent construire un circuit de karting en forme de 8... de ces deux circuits lequel est le plus long
    13·1 answer
  • What is the Decimal Equivalent to 1/3?
    7·1 answer
  • What is the probability that Saturday is the day after Wednesday?
    9·2 answers
  • Find the value of x in the following system of equations:
    9·1 answer
  • HOW TO PUT GRAPH INTO SLOPE INTERCEPT FORM
    8·1 answer
  • 1. The backdrop of the altar in a church is triangular in shape. It has a base of 10.5 meters
    6·1 answer
  • What is the distance between (4, 3) and (7, 3)?
    9·2 answers
  • The equation h = 7 sine (startfraction pi over 21 endfraction t) 28 can be used to model the height, h, in feet of the end of on
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!