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
Llana [10]
2 years ago
8

A simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week

. Of the 250 employed individuals​ surveyed, 41 responded that they did work at home at least once per week. Construct a​ 99% confidence interval for the population proportion of employed individuals who work at home at least once per week.
Mathematics
1 answer:
Levart [38]2 years ago
7 0

Answer:

99% confidence interval for the population proportion of employed individuals is [0.104 , 0.224].

Step-by-step explanation:

We are given that a simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week.

Of the 250 employed individuals​ surveyed, 41 responded that they did work at home at least once per week.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                              P.Q. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of individuals who work at home at least once per week = \frac{41}{250} = 0.164

           n = sample of individuals surveyed = 250

<em>Here for constructing 99% confidence interval we have used One-sample z proportion statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5%

                                             level of significance are -2.5758 & 2.5758}  

P(-2.5758 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 2.5758) = 0.99

P( -2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

P( \hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.99

<em>99% confidence interval for p</em> = [\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }]

= [ 0.164-2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } } , 0.164+2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } } ]

 = [0.104 , 0.224]

Therefore, 99% confidence interval for the population proportion of employed individuals who work at home at least once per week is [0.104 , 0.224].

You might be interested in
I need an explanation plzzz help :)
just olya [345]

Answer:

117.6 ft

Step-by-step explanation:

You have two legs of the triangle and an angle, so you'll use tangent here. Sin and cos both involve hypotenuse, which you're not given.

Remember SOHCAHTOA

Tangent = Opposite / Adjacent

The side opposite the angle is the height, the side adjacent to the angle is the 25 ft.

tan(78°) = height / 25

25tan(78°) = height = 117.6 ft.

3 0
2 years ago
Read 2 more answers
4. Adrian and Rory started comic book collections at the same time. Adrian
PilotLPTM [1.2K]

As both are adding same number of comic books each months, they will not have same number of books. Adrian will have 4 more comic books.

Step-by-step explanation:

Given,

Adrian starts with 12 comic books and add 4 each month.

Let,

m be the number of books.

A(m) = 4m+12

Rory starts with 8 comic books and add 4 comic books each month.

R(m) = 4m+8

As both are adding same number of comic books each months, they will not have same number of books. Adrian will have 4 more comic books.

6 0
3 years ago
Situation 1: Two students, Theo and Lance, each have some chocolates. They know that
vivado [14]

They each have two chocolates so those numbers of chocolates are the same.

Not counting the tubs, Arthur has one bag of chocolates and 25 loose chocolates; Oliver has two bags and 7 loose. If they both have the same total number of chocolates, then the difference in the number of loose chocolates they have (25-7=18) must be the number of chocolates in a bag.

There is no information given, in the problem as you show it, that allows us to determine the number of chocolates in a tub.

Answers: chocolates in a bag: 18. chocolates in a tub: unknown.

4 0
3 years ago
August hosted two dinner parties for his friends. Twenty guests attended the first party, and twenty-eight guests attended the s
Neporo4naja [7]
25+25x=27 
<span>25x=2 </span>
<span>x=2/25 </span>
<span>x=.08 </span>
<span>8%</span>
8 0
3 years ago
What can be multiplied to get 40 but also added to get 29​
Tresset [83]

Answer:

is that even possible.

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • The ratio of nitrogen to potassium in a sample of soil is 9;12. The sample has 48 units of nitrogen . How much potassium does th
    12·1 answer
  • Please explain . solve the system by elimi ation -x-18y=-3 7x-9y=21
    6·1 answer
  • Solve y^2 + 4y - 32 = 0 using the zero product property.
    15·1 answer
  • Calculate the average rate of change for the given graph from x = –2 to x = 0 and select the correct answer below.
    12·1 answer
  • The volume of a cube is found by using the formula Alta third power where else side length if the side length is 4X to the third
    5·1 answer
  • Do It! Review 16-1 During the current month, Wacholz Company incurs the following manufacturing costs. (a) Purchased raw materia
    13·1 answer
  • How many time can 21 go into 6
    8·2 answers
  • Put the quadratic
    12·1 answer
  • There are 4 cups of flour in 3 batches of cookies . How many cups are in one batche.
    9·2 answers
  • Please help me on this​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!