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
Dima020 [189]
3 years ago
15

A news organization conducted a survey about preferred methods for obtaining the news. A random sample of 1,605 adults living in

a certain state was selected, and 16.2 percent of the adults in the sample reported that television was their preferred method. Which of the following is an appropriate margin of error for a 90 percent confidence interval to estimate the population proportion of all adults living in the state who would report that television is their preferred method for obtaining the news?
Mathematics
1 answer:
JulijaS [17]3 years ago
5 0

Answer:

ME= 1.64 *\sqrt{\frac{0.162*(1-0.162)}{1605}}=0.015

Step-by-step explanation:

Notation and definitions  

n=1605 random sample taken  

\hat p=0.162 estimated proportion of adults in the sample reported that television was their preferred method

p true population proportion of adults in the sample reported that television was their preferred method

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})  

In order to find the critical values we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.9=0.1 and \alpha/2 =0.05. And the critical values would be given by:  

z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64  

The margin of error for the proportion interval is given by this formula:  

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

And if we replace the values we got:

ME= 1.64 *\sqrt{\frac{0.162*(1-0.162)}{1605}}=0.015

You might be interested in
Use the drop-down menus to complete each equation so the statement about its solution is true.
disa [49]

Answer:


Step-by-step explanation:

So,it would be easier to simplify the right equation, so when I say "the right equation", I mean the one I will make right now. It is 8x+9. So the first problem is 8x+9=x+?. Well, if there are no solutions, the slopes have to be the same, and the y-int doesn't matter. So the answer would be + 7x because that will make the x an 8x. If there is one solution, then the slope has to be different. So literally anything but 7x will work. Even constants. If there are infinitely many solutions, then the equations have to be the same. Meaning, you would have to add 7x and 9 to make the left equation the same as the right.

6 0
3 years ago
Combine these unlike fractions, then simplify. 3/8+1/6 explain plz
larisa86 [58]

Answer: 13/24

Step-by-step explanation:

3/8 + 1/6 = 9/24 + 4/24

9 + 4/24 = 13/24

Decimal Form = 0.541667

Hope this helps! #BaconSquad

4 0
3 years ago
Ann took a taxi home from the airport. The taxi fare was \$2.10$2.10 per mile, and she gave the driver a tip of \$5$5. Ann paid
Stolb23 [73]

Answer:

If your wondering how many miles the taxi drove the answer is 21 miles

Step-by-step explanation:


5 0
3 years ago
Please help with this question
alexgriva [62]
A = 1/2 BH

#17
B = 3 H = 4
A = 1/2 BH
A = 1/2 (3)(4) = 6

#18
B = 6 H = 4
A = 1/2 BH
A = 1/2 (6)(4) = 12

#19
B = 12 H = 8
A = 1/2 BH
A = 1/2 (12)(8) = 48

#20
B = 11 H = 5
A = 1/2 BH
A = 1/2 (11)(5) = 27.5

3 0
3 years ago
HOW DO YOU DO THIS??????????
Alexeev081 [22]
From 9:00 am to 9:00pm, that's a total of 12 hours, 
so 12 of the 20 hours are charged at a rate of 0.25 dollar per hour, and the other 8 hours (20-12=8) are charged at a rate of $0.06 per hour.
the answer is b. 
it should be 0.06 though, not 0.6
5 0
3 years ago
Other questions:
  • What is one third of 1080
    13·2 answers
  • Emily is encouraged to read more than 4 hours each week. It takes her 45 minutes to finish her first book. She divides the remai
    12·1 answer
  • Estimate the following deference using front-end estimation.PLS HURRY!<br><br> 788.44 - 225.6
    12·1 answer
  • What is y = |x+2| - 4
    7·1 answer
  • Can someone help me ?
    6·1 answer
  • In the list of numbers, 6, x, 10, 2, 7, 13, and 15, the median is 10.
    8·1 answer
  • A diver was swimming 62 feet below sea level. He then dove 39 feet further down. He ascended 48 feet after a while. Find the new
    13·1 answer
  • What can even numbers always be divided by?
    12·1 answer
  • Please help me with both! would really appreciate it
    8·1 answer
  • Dante runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!