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
Mars2501 [29]
3 years ago
9

According to a Washington Post-ABC News poll, 331 of 502 randomly selected U.S. adults interviewed said they would not be bother

ed if the National Security Agency collected records of personal telephone calls they had made. Is there sufficient evidence to conclude that a majority of U.S. adults feel this way? Test the appropriate hypotheses using a .01 significance level.
Mathematics
1 answer:
k0ka [10]3 years ago
4 0

Answer:

z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124  

p_v =P(z>7.124)=5.24x10^{-13}  

So the p value obtained was a very low value and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.  

Step-by-step explanation:

Data given and notation

n=502 represent the random sample taken

X=331 represent the adults that said they would not be bothered if the NAtional security agency

\hat p=\frac{331}{502}=0.659 estimated proportion of people who would not be bothered if the NAtional security agency

p_o=0.5 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 the majority of 0.5:  

Null hypothesis:p\leq 0.5  

Alternative hypothesis:p > 0.5  

When we conduct a proportion test we need to use the z statistic, 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{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124  

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>7.124)=5.24x10^{-13}  

So the p value obtained was a very low value and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.  

You might be interested in
What is 0.36 with a line over top expressed as a fraction in simplest form
s344n2d4d5 [400]
9/25 I don’t really know
8 0
2 years ago
What's is the proablity of drawing a black card or any ten on a single random draw from a standard 52-card deck
SCORPION-xisa [38]
Your book has the answers
8 0
2 years ago
Solve the system of equations. Use any method you prefer <br><br> y = 2x + 5<br><br> -2x - y = - 1
Liula [17]
Please please help please help me please please help me



1
8 0
2 years ago
Find the value of x that makes the quadrilateral a parallelogram <br><br> 2x+5=3x
Colt1911 [192]
The answer would be 5
7 0
3 years ago
Read 2 more answers
What is everyones favorite UNDERTALE character
gogolik [260]

Answer:

flowey the flower (aka: Asriel Dreamer)

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • Write the equation of the line that is parallel to the graph of Y=1/2 X +6 and his Y intercept is -2
    14·1 answer
  • W much a quantity changes
    11·1 answer
  • When Arjun makes hot cocoa, he adds 20 mL 20 mL20, start text, space, m, L, end text of chocolate syrup for every 3 33 ounces of
    9·1 answer
  • What is equal to 0.25
    10·1 answer
  • What is the solution to the system of equations? y = –5x + 3 y = 1 (0.4, 1) (0.8, 1) (1, 0.4) (1, 0.8)
    8·2 answers
  • A textbook store sold a combined total of 473 chemistry and sociology textbooks in a week. The number of sociology textbooks sol
    14·1 answer
  • Convert 4.5 into second step by step please ​
    5·2 answers
  • Can someone help me with this thank you
    13·2 answers
  • please just help me and give correct answer and not a wrong short answer i need just explanation and please tell me for each ans
    12·1 answer
  • To increase sales, an online clothing store began giving a 50% off coupon to random customers. Customers didn't know whether the
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!