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
qwelly [4]
2 years ago
7

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,91

1 of them had no strategic business plan. a) Use a 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans. Give an interpretation of this interval. (5 Points) b) Would a 99% confidence interval be wider or narrower than the one you calculated in part (a)
Mathematics
1 answer:
Maurinko [17]2 years ago
3 0

Answer:

a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

b) Wider

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 z-score that has a p-value of 1 - \frac{\alpha}{2}.

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.

This means that n = 3900, \pi = \frac{1911}{3900} = 0.49

90% confidence level

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

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032

The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

Question b:

The margin of error is:

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

The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.

You might be interested in
I need help “ write the following answer as a fraction :
lubasha [3.4K]

Answer:

1/16

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the value of f(2)?
Airida [17]

Answer:

The value of f(2) is 1

Step-by-step explanation:

4 0
3 years ago
What is 2 3/10 as a percent?
kobusy [5.1K]
2 3/10 = 2.3
To get this number as a percent, we need to multiply it by 100: 2.3 is a whole number, and can be represented by fraction 2.3/1
A percentage is represented by a fraction over 100. So to transform 2.3/1 to a percentage, just multiply both numerator and denominator by 100, and you'll get 230/100.
So 2 3/10 is 230% as a percent.

Hope this Helps! :)
4 0
3 years ago
Read 2 more answers
Need helpPlzzzzzzzzzzzzzzzz
Radda [10]

Answer:

2

Step-by-step explanation:

7 0
3 years ago
ILL GIVE BRAINLIEST!!!<br><br> No need for explanation, just an answer is fine. Thank you.
Naddika [18.5K]

Answer:

10

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • HELP ASAP!!
    13·1 answer
  • 5(x −1) &lt; 3x + 10 − 8x
    8·2 answers
  • Hlp if u know the answer
    14·2 answers
  • are the deer near anyone else getting really brave and not caring about vehicles much anymore? i feel a deer uprising coming soo
    6·1 answer
  • a. What are the expected returns of the two​ stocks? b. What are the standard deviations of the returns of the two​ stocks? c. I
    9·1 answer
  • Margot used
    10·1 answer
  • Match the terms to their definition.
    5·1 answer
  • Algebra 2
    10·1 answer
  • I need help with math ​
    8·1 answer
  • Find the slope of the line that passes through (8, 4) and (5, 2).
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!