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
vlabodo [156]
2 years ago
8

Suppose the survey was based on a sample of 700 companies. Find the 80% confidence interval for the proportion of all companies

likely to require higher employee contributions for health care coverage. Find the LEFT endpoint and RIGHT endpoint.
Mathematics
1 answer:
Angelina_Jolie [31]2 years ago
6 0

Answer:

0.61 - 1.28\sqrt{\frac{0.61(1-0.61)}{700}}=0.586

0.61 + 1.28\sqrt{\frac{0.61(1-0.61)}{700}}=0.634

The 80% confidence interval would be given by (0.586;0.634)

Step-by-step explanation:

A recent survey showed that 61% of U.S. employers were likely to require higher employee contributions for health care coverage. Suppose the survey was based on a sample of 700 companies. Find the 80% confidence interval for the proportion of all companies likely to require higher employee contributions for health care coverage.

Previous concepts

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{p(1-p)}{n}})

Solution to the problem

In order to find the critical value 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 80% of confidence, our significance level would be given by \alpha=1-0.80=0.2 and \alpha/2 =0.1. And the critical value would be given by:

z_{\alpha/2}=-1.28, z_{1-\alpha/2}=1.28

The confidence interval for the mean is given by the following formula:  

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

If we replace the values obtained we got:

0.61 - 1.28\sqrt{\frac{0.61(1-0.61)}{700}}=0.586

0.61 + 1.28\sqrt{\frac{0.61(1-0.61)}{700}}=0.634

The 80% confidence interval would be given by (0.586;0.634)

You might be interested in
What is the value found using the linear​ approximation? ln(0.93) ≈
Vinil7 [7]

Answer:

I think its 0.9 I believe so

3 0
2 years ago
Evaluate the limit by first recognizing the sum as the Riemann sum for a function defined on the interval [0,1]: lim as n approa
mina [271]
\lim_{n \to +\infty} \left ( \dfrac{1}{n} \cdot \left ( \sqrt{ \dfrac{1}{n} } + \sqrt{ \dfrac{2}{n} } + \sqrt{ \dfrac{3}{n} } + \cdots + \sqrt{ \dfrac{n}{n} }} \right ) \right ) =

\dfrac{1}{n} \sum_{i = 1}^n \left (  \sqrt{ \dfrac{i}{n} }   \right ) =  \int\limits^1_0 { \sqrt{x} } \, dx  =  \left [  \frac{2}{3}x^{ \frac{3}{2} }       \right ]^{1}_{0} =   \dfrac{2}{3} \cdot 1^{ \frac{3}{2} }  -  \dfrac{2}{3} \cdot 0^{ \frac{3}{2} }  =  \boxed{ \dfrac{2}{3} }
3 0
2 years ago
1.What is value of x?
Vesnalui [34]
For the first picture..........

|AB| |BD|
-----=-----
|AC| |DC|

x+8 10
-----=----
2x-5 14

10(2x-5)=14(x+8)

20x-50 = 14x+112

20x-14x = 112+50

6x = 162

x= 162/6

x=27.....

For the second picture.......

AD| |AC|
-----=-----
|DB| |CB|

3 4
--=---
x 7.5

4×X = 3×7.5

x = 22.5/4

x = 5.625....
5 0
3 years ago
PLEASE HELP!! BRAINLIEST ANSWER AND FASTEST ANSWER GETS TON OF FREE POINTS...MATH WHIZZES, HELP ME OUT. FORGOT HOW TO DO THIS.
Julli [10]
Inscribed angles equal half of their arc length. So <D+ <B = 180
substitute: x+24+x+10 = 180 
solve: 2x + 34 = 180
2x= 146
x= 73
NOw find the measure of angle A:
<a = x + 15
<a = 73 + 15
<a = 88
 Now to find <C
<C = 180- 88
<C = 92
Hope this helps!
5 0
2 years ago
Find the zero of the linear function F(x)=-4x+5
Sholpan [36]

Answer:um....

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • 1/8 in simplest forn as a percent fraction amd decimal
    15·1 answer
  • What is tanA?<br><br> A. 15/17<br><br> B. 8/17<br><br> C. 8/15<br><br> D. 15/8
    13·2 answers
  • Find the Greatest Common Factor of 3a^2+9
    6·2 answers
  • 3. (2.56 x 10^6) x (3.56 x 10^2) =
    7·2 answers
  • What is the slope parallel to the equation: y=4x+3​
    10·1 answer
  • You start at (3, 5). You move down 4 units and left 1 unit. Where do you end?​
    14·1 answer
  • The nurse is preparing to administer filgrastim to a client with leukemia who weighs 60 kg. The prescribed dose is 5 mcg/kg/day.
    8·1 answer
  • 2/12= blank 48 gffnvbnvbnvbfffnvbnbvffffffffbvcnffffffffffnbvnvbnbvnbvffffffffffffffffff
    11·1 answer
  • Solve the following multi-step equation: 2(z + 5) + 4 = -12 What does z equal?
    11·1 answer
  • The movie ended at 7:05 p.m. and lasted 2 hours 40 minutes. What time did the movie begin?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!