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
netineya [11]
2 years ago
8

Gun ownership Concerned about recent incidence of gun violence, a public interest group conducts a poll of 850 randomly selected

American adults and finds that 44% of those surveyed have a gun in their home.
a. Construct and interpret a 95% confidence interval for the proportion of all American adults who have a gun in their home.
b. Explain what is meant by 95% confidence in this context.
Mathematics
1 answer:
denis23 [38]2 years ago
5 0

Answer:

a.

The 95% confidence interval for the proportion of all American adults who have a gun in their home is (0.4066, 0.4734). This means that we are 95% sure that the true population proportions of American adults who have a gun in their home is between these two values.

b.

The confidence level is the probability of the confidence interval containing the population proportion.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

Poll of 850 randomly selected American adults and finds that 44% of those surveyed have a gun in their home.

This means that n = 850, \pi = 0.44

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.44 - 1.96\sqrt{\frac{0.44*0.56}{850}} = 0.4066

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.44 + 1.96\sqrt{\frac{0.44*0.56}{850}} = 0.4734

The 95% confidence interval for the proportion of all American adults who have a gun in their home is (0.4066, 0.4734). This means that we are 95% sure that the true population proportions of American adults who have a gun in their home is between these two values.

b. Explain what is meant by 95% confidence in this context.

The confidence level is the probability of the confidence interval containing the population proportion.

You might be interested in
The sum of the squares of 3 consecutive positive integers is 116. What are the numbers?
Nonamiya [84]
<span>let the numbers be 2n-2,2n,2n + 2 then sum of squares will be 12 n ^2 + 8 = 116 which implies n = 3.numbers are 4,6,8 </span>
3 0
3 years ago
Read 2 more answers
The temperature at 4 a.m. was -13 °F. The temperature was rising at a steady rate of 5 °F an hour. At what time will the tempera
lara [203]

I believe the correct answer is that the temperature will be 12 degrees F at 9 A.M. I hope this helps!

7 0
3 years ago
Read 2 more answers
A 4 foot tree was planted in 2012 outside a high school. The tree grew continuously by 22% each year from that point. Find out w
Brut [27]

Answer:

The height of the tree in 2020 was of 19.63 feet.

Step-by-step explanation:

Exponential equation for growth:

The exponential equation for the growth of an amount has the following format:

H(t) = H(0)(1+r)^t

In which H(t) is the amount after t years, H(0) is the initial amount and r is the growth rate, as a decimal.

A 4 foot tree was planted in 2012 outside a high school.

This means that H(0) = 4

The tree grew continuously by 22% each year from that point.

This means that r = 0.22

Find out what the height of the tree was in 2020.

2020 is 2020 - 2012 = 8 years after 2012, so this is H(8).

H(t) = H(0)(1+r)^t

H(t) = 4(1+0.22)^t

H(4) = 4(1.22)^t

H(4) = 4(1.22)^8 = 19.63

The height of the tree in 2020 was of 19.63 feet.

6 0
3 years ago
What is another name for 23 ten thousands?
kicyunya [14]
<span>230,000

</span>Hope I Helped You!!! :-)

Have A Good Day!!!
3 0
2 years ago
Read 2 more answers
Find the area of the unshaded region for these two problems​
Grace [21]

1. Area of the right angled ∆ = 1/2 × base × height

height = 16m

base = √20² – 16²

= √400 –256

= √144

= 12 m

Area of the unshaded portion

= 1/2 × base × height

= 1/2 × 12 × 16

= 96m²

2. Area of the rectangle = 300ft × 150ft

= 45000sq. ft

Area of the shaded portion = 100² + (1/2×b×h)

= 10000 + (1/2×120×150)

= 10000 + 9000

= 19000 sq. ft

Area of the unshaded part of the rectangle

= (45000 – 19000)sq. ft

= 26000 sq. ft

5 0
2 years ago
Other questions:
  • Christian plays outside for 4/5 hour. For 1/2 of that time, he plays basketball. What fraction of an hour did he play basketball
    11·1 answer
  • Simplify into one fraction
    13·2 answers
  • I have another math question and another Brainliest for a math genius
    10·2 answers
  • When simplified, (2x + 3)(7x – 1) + (2x – 4) is:
    12·1 answer
  • Determine the standard form of the equation of the line that passes through (-7,8) and (0,2)
    8·1 answer
  • I need help with this question
    13·1 answer
  • HURRY WILL MARK BRAINLIEST AND CASHAPP MONEY
    7·2 answers
  • IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A sample of 13 people is selected at rando
    12·1 answer
  • A square has side of length y units what is the area?
    14·1 answer
  • A toilet is leaking at the rate of 1 fluid ounces per minute. How many gallons is
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!