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
Ipatiy [6.2K]
3 years ago
11

We would like to create a confidence interval.

Mathematics
1 answer:
Vlada [557]3 years ago
6 0

Answer:

c.A 90% confidence level and a sample size of 300 subjects.

Step-by-step explanation:

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

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

In which

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

In this problem

The proportions are the same for all the options, so we are going to write our margins of error as functions of \sqrt{\pi(1-\pi)}

So

a.A 99% confidence level and a sample size of 50 subjects.

n = 50

99% confidence interval

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The margin of error is

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{2.575}{\sqrt{50}}\sqrt{\pi(1-\pi)} = 0.3642\sqrt{\pi(1-\pi)}

b.A 90% confidence level and a sample size of 50 subjects.

n = 50

90% confidence interval

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The margin of error is

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{1.645}{\sqrt{50}}\sqrt{\pi(1-\pi)} = 0.2623\sqrt{\pi(1-\pi)}

c.A 90% confidence level and a sample size of 300 subjects.

n = 300

90% confidence interval

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The margin of error is

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{1.645}{\sqrt{300}}\sqrt{\pi(1-\pi)} = 0.0950\sqrt{\pi(1-\pi)}

This produces smallest margin of error.

d.A 99% confidence level and a sample size of 300 subjects.

n = 300

99% confidence interval

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The margin of error is

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{2.575}{\sqrt{300}}\sqrt{\pi(1-\pi)} = 0.1487\sqrt{\pi(1-\pi)}

You might be interested in
The numbers on two consecutively numbered gym lockers have a sum of 133.
kherson [118]

Answer:

66 and 67 are the answers

6 0
2 years ago
One of the altitudes of the parallelogram shown is StartRoot 22.5 EndRoot units. What is the length of the other altitude?
aksik [14]

Answer:

the length of the other altitude of the given parallelogram will be 6 units and option B is the correct choice.

6 0
2 years ago
Read 2 more answers
Easy question :)
bulgar [2K]
C. because 2.25 X 3 = 6.75 and 6.75 X 3 is 20.25
3 0
3 years ago
Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, fi
scZoUnD [109]

Answer:

A

Step-by-step explanation:

6 0
3 years ago
Sammy’s dad drove their car 150 miles in three hours. At this rate, how far would he drive in nine hours?
PilotLPTM [1.2K]

Answer:

distance in 3 hours = 150 miles

distance in 1 hour = 150/3 = 50 miles

distance in 9 hours = 50 × 9 = 450 miles

4 0
2 years ago
Read 2 more answers
Other questions:
  • What is the value of the function f(x) = 2x^2 + 3 when x = 2?
    6·2 answers
  • How do you write 0.28 as a percentage
    10·2 answers
  • Can you help me with this problem I can't find it out
    8·2 answers
  • Which term shows a product of a number and a variable? 5 + 6x - 7 + 4 <br> A. 5 B. 6x C. -7 D. 4
    13·2 answers
  • If 20% of all manually filed returns contain errors, and 0.05% of all electronically filed returns contain errors, how much more
    13·2 answers
  • 7782 rounded to the nearest hundred
    14·2 answers
  • What is the degree of the monomial? 5n3
    5·1 answer
  • At my favorite computer store, there was a sale of 20% off. I bought a $300
    6·1 answer
  • Complete the statement: In a glide reflection, the direction of the ______ must be parallel to the line of reflection.
    9·1 answer
  • PLEASE HELP
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!