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]
3 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]3 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
3900 workers in 3 buildings. twice as many work in largest building as the smallest of the 3 . there are 500 more workers in the
Svetllana [295]
<h3><u>Question:</u></h3>

There are 3900 workers in the three main buildings downtown. Twice as many people work in the largest building as in the smallest of the three. There are 500 more workers in the second-largest building than in the smallest building. How many workers are in each building?

<h3><u>Answer:</u></h3>

There are 850 workers in smallest building and 1700 workers in largest building and 1350 workers in second largest building

<h3><u>Solution:</u></h3>

Let "b" be the number of workers in smallest building

Given that Twice as many people work in the largest building as in the smallest of the three

number of workers in largest building = 2b

Given that There are 500 more workers in the second-largest building than in the smallest building

Number of workers in second largest building = 500 + b

Given that there are 3900 workers in 3 buildings

b + 2b + 500 + b = 3900

4b + 500 = 3900

4b = 3900 - 500

4b = 3400

b = 850

Thus there are 850 workers in smallest building

workers in largest building = 2b = 2(850) = 1700

workers in second largest building = 500 + b = 500 + 850 = 1350

Thus there are 850 workers in smallest building and 1700 workers in largest building and 1350 workers in second largest building

6 0
3 years ago
F(x) = cot x PRE CALC HELP PLS?!
alisha [4.7K]
Check the picture below.

is it even?  well, even functions use the y-axis as a mirror, so a pre-image on the right-side, will be a mirror of the image on the left-side, but in this case it isn't so, if you put a mirror right on the y-axis, the left-side will look a bit different.

does it have a zero at x = 0?  well, just look at the graph, is the line touching the x-axis at 0? nope.

does it have an asymptote at 0?  well, surely you can see it right there.

8 0
3 years ago
Which equation has a slope
Dominik [7]
All the choices are in the slope-intercept form where,

y=mx+b

so, the number before the x is the slope. The given slope is -34. We just have to look for the -34 number before the x. So mong the choices, it is the letter a choice that has the slope -34. So the answer is A.
7 0
3 years ago
Read 2 more answers
In my number, both digits are even numbers. The digit in the tens place is less than the digit in the ones place. The sum of the
valina [46]

Answer:

I think it's 24.

Step-by-step explanation:

2 and 4 are both even numbers. 2, the digit in the tens place is less than 4, the digit in the ones place. 2 + 4 = 6

Hope this helps!

8 0
3 years ago
I don’t understand this
Inessa05 [86]

Answer:

54

Step-by-step explanation:

18 inches per year * 3 years = 54 inches

5 0
3 years ago
Read 2 more answers
Other questions:
  • 1 pound of apples for $2.15 or 3 pounds of apples for $5.76
    15·1 answer
  • What is the interquartile range of the following data set? 46, 9, 48, 96, 61, 84, 29, 1, 82, 5, 34
    5·1 answer
  • Write an counter example for the statement: all square roots are rational numbers
    14·2 answers
  • Is 5359 divisible by 4
    9·2 answers
  • An experiment was conducted to evaluate the success of an Ebola virus vaccine. The subjects were unaware of the treatment they w
    11·1 answer
  • Four dollars more than seven times Julie's amount of money.
    14·1 answer
  • Solve for X please help
    10·2 answers
  • Elena paints the back of a aquarium it has a height of 1 3/4 feet the painted area is 5 5/6 what is the length
    6·1 answer
  • Can I get help on this one
    14·2 answers
  • What is the area of the parallelogram QRST?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!