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
What is 2∙ 2∙ 2∙ 2∙ 2∙ 2∙ 2∙ 2∙ 2 in exponential form?
Lubov Fominskaja [6]

Answer:

2^9

Step-by-step explanation:

Since there are nine 2s being multiplied by each other, we can represent this as 2^9.

5 0
2 years ago
Read 2 more answers
Roberto has 2 books with 319 pages each and 3 books with 264 pages.How many pages are all in together.
34kurt
2(319) +3(264) = 1430

There are 1,430 pages. 
4 0
2 years ago
Read 2 more answers
If you are a student with no assets of any value and have liability insurance on an old car that pays a maximum of $50,000 per a
svetoff [14.1K]

Answer:

D

Step-by-step explanation:

they will sue for the rest of the money, because they are entitled to it if you are the cause of an accident.

6 0
3 years ago
Jason has 34 blueberry scones and 85 raspberry scones. There is 17 bags of scones each filled with an equal amount of blueberry
ozzi

Answer:

2 blueberry and 5 raspberry scones go in each bag

Step-by-step explanation:

34+85=119

119/17=7

34/85= 2/5

so 2 blueberry and 5 raspberry scones go in each bag

hope that helps :)

8 0
2 years ago
Read 2 more answers
If P(A)=2/3, P(B)=4/5, and P(A U B) =11/15, what is P(A ∩ B)?
Juliette [100K]
The answer is A on apex 
3 0
3 years ago
Read 2 more answers
Other questions:
  • Alana spent 21 dollars of her 300 dollar paycheck on a gift . What percent of her paycheck was spent on the gift
    12·1 answer
  • In a typical symphony orchestra, 16 out of every 100 musicians are violinists. What fraction of the orchestra are violinists?
    12·1 answer
  • What is 40 times 103
    8·2 answers
  • Solve for x 2/5x= 10
    6·1 answer
  • Write a definite integral that represents the area of the region. (Do not evaluate the integral.)
    15·1 answer
  • Blanks ?? Help me ??
    7·1 answer
  • When a number is added to the set of numbers 7,8,9,12,6,10 and 11, the mean becomes 8. What number was added
    6·1 answer
  • If cos a= 0.93. Sin 0 =0.26, and tan ß = 0.84, find a + B + 0.
    14·1 answer
  • Solve for x: 8x = 2/3<br>solve for x: 1/4x =5​<br>two questions
    13·1 answer
  • Determine the slope of the line that contains the given points.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!