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
Gelneren [198K]
2 years ago
8

A national survey conducted in 2011 among a simple random sample of 1,507 adults shows that 56% of Americans think the Civil War

is still relevant to American politics and political life.(a) Conduct a hypothesis test to determine if these data provide strong evidence that the majority of the Americans think the Civil War is still relevant.(b) Interpret the p-value in this context.(c) Calculate a 90% confidence interval for the proportion of Americans who think the Civil War is still relevant. Interpret the interval in this context, and comment on whether or not the confidence interval agrees with the conclusion of the hypothesis test.
Mathematics
1 answer:
Drupady [299]2 years ago
7 0

Answer:

a)z=4.658

p_v =P(z>4.65)=1-P(z  

b) Using the significance level assumed \alpha=0.05 we see that p_v so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life is  higher than 50%.

c) The 90% confidence interval would be given (0.527;0.593).

We are confident that about 54% to 59% of all Americans think the Civil War is relevant.

Step-by-step explanation:

I )Part a

1) Data given and notation

n=1507 represent the random sample taken  

X represent the Americans who thinks that the Civil War is still relevant to American politics and political life

\hat p estimated proportion of Americans who thinks that the Civil War is still relevant to American politics and political life in the sample

p_o=0.5 is the value that we want to test since the problem says majority    

\alpha=0.05 represent the significance level (no given, but is assumed)  

z would represent the statistic (variable of interest)  

p_v represent the p value (variable of interest)  

p= population proportion of Americans who thinks that the Civil War is still relevant to American politics and political life

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life exceeds 50%(Majority). :  

Null Hypothesis: p \leq 0.5

Alternative Hypothesis: p >0.5

We assume that the proportion follows a normal distribution.  

This is a one tail upper test for the proportion of  union membership.

The One-Sample Proportion Test is "used to assess whether a population proportion \hat p is significantly (different,higher or less) from a hypothesized value p_o".

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np_o =1507*0.5=753.5>10

n(1-p_o)=1507*(1-0.5)=753.5>10

3) Calculate the statistic  

The statistic is calculated with the following formula:

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

On this case the value of p_o=0.5 is the value that we are testing and n = 1507.

z=\frac{0.56 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1507}}}=4.658

The p value for the test would be:

p_v =P(z>4.65)=1-P(z  

II) Part b

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.  

Based on the alternative hypothesis the p value would be given by:

p_v =P(z>4.65)=1-P(z  

Using the significance level assumed \alpha=0.05 we see that p_v so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life is  higher than 50%.

III) Part c

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 90% confidence interval the value of \alpha=1-0.9=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.58

And replacing into the confidence interval formula we got:

0.56 - 2.58 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.527

0.56 + 2.58 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.593

And the 90% confidence interval would be given (0.527;0.593).

We are confident that about 54% to 59% of all Americans think the Civil War is relevant.

And this result agrees with the result of part b, since the interval not contains the value of 0.5 we can conclude that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life it's higher than 0.5 at 90% of confidence.

You might be interested in
What is DE? Put the answer below.<br><br> DE =
FinnZ [79.3K]

Answer:

DE = 55

Step-by-step explanation:

As you can see from the red marks showing that the lengths of each triangle are the same, it must also be true that E is equal to 55.

4 0
3 years ago
Cynthia is mowing lawns for extra money. The amount of money she made after putting gas in the lawnmower is shown below.
Nimfa-mama [501]

Answer:

a

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Describe in words the similarities and differences in multiplying and dividing complex numbers.
iragen [17]

Answer:

t does not matter if the two numbers are the same for multiplication or division. 4. ( ÷ ) To divide two fractions, take the second fraction, and flip it so that the top number is now on the bottom and vice versa, then multiply the two fractions together like you would for number 3.

Step-by-step explanation:

7 0
3 years ago
Calculate the percent of change: 50 pounds to 35 pounds.
Vladimir [108]
30 percent change is the answer
7 0
3 years ago
A list of numbers is given <br><br><br> 32,16,8,4,2,1<br><br> Write a rule for the pattern
Sphinxa [80]
It is subtracting the current number by 1/2    OR you can divide by 2. each time.

32 / 2= 16
16 / 2=8
8/2=4
4/2=2
2/2=1

Hope this helped!
5 0
3 years ago
Read 2 more answers
Other questions:
  • 8. What is the point-slope form of a line passing through the point (-2.5) with the same slope as
    9·1 answer
  • Timmy saved his money for a whole month. In week 1 he saved 10$. In week 2 he saved 15$. In week 3 he saved 8$. and in week 4 he
    15·2 answers
  • Pleaaseeee help me :/
    6·1 answer
  • The expression two square root of three minus square root of 27 is equivalent to
    13·2 answers
  • What is the diffrence between 48 degrees Fahrenheit and -13 degrees fahrenheit​
    8·1 answer
  • HELP ASAP NOOOOOOOOOOOOWWW!!!!!!!!!!! 30 POINTS
    13·2 answers
  • jasmine has all nickels x and dimes y in her coin jar. if she has 36 coins in all, and four more dimes than. nickels find how mu
    14·2 answers
  • The lunch special at Scott's Restaurant is a sandwich, a drink and a dessert. There are 3 sandwiches, 1 drink, and 2 desserts to
    13·1 answer
  • Which expressions are equivalent?
    10·2 answers
  • Write each polynomial in standard form. Then give the leading coefficient. You may need to combine like terms before writing the
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!