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
Alla [95]
3 years ago
11

From a survey of coworkers you find that 36​% of 200 have already received this​ year's flu vaccine. An approximate 95​% confide

nce interval is ​(0.293​, 0.427​). ​a) How would the confidence interval change if the sample size had been 1800 instead of 200​? ​b) How would the confidence interval change if the confidence level had been 90​% instead of 95​%? ​c) How would the confidence interval change if the confidence level had been 98​% instead of 95​%?
Business
1 answer:
sveta [45]3 years ago
7 0

Answer:

Part a: <em>By increasing the sample size for same confidence level, the confidence interval is reduced.</em>

Part b: <em>By reducing the confidence level for same sample size, the confidence interval is reduced.</em>

Part c: <em>By increasing the confidence level for same sample size, the confidence interval is increased.</em>

Explanation:

Part a

As from given data

  • Percentage of co-workers already received flu vaccine p=0.36,
  • n=1800

The confidence interval is given as

CI=\hat{p} \pm z_{\alpha}\sqrt{\frac{p(1-p)}{n}}

Here

  • z is given for 95% confidence level as 1.960

By substituting values in the equation

CI=\hat{p} \pm z_{\alpha}\sqrt{\frac{p(1-p)}{n}}\\CI=0.36 \pm 1.960\sqrt{\frac{0.36(1-0.36)}{1800}}\\CI=0.36 \pm 0.02217\\CI=(0.3378,0.3812)

It is evident that the confidence interval is smaller, indicating a lesser chance of error.

<em>This means that by increasing the sample size for same confidence level, the confidence interval is reduced.</em>

Part b

As from given data

  • Percentage of co-workers already received flu vaccine p=0.36,
  • n=200

The confidence interval is given as

CI=\hat{p} \pm z_{\alpha}\sqrt{\frac{p(1-p)}{n}}

Here

  • z is given for 90% confidence level as 1.645  

By substituting values in the equation

CI=\hat{p} \pm z_{\alpha}\sqrt{\frac{p(1-p)}{n}}\\CI=0.36 \pm 1.645\sqrt{\frac{0.36(1-0.36)}{200}}\\CI=0.36 \pm 0.0557\\CI=(0.3043,0.4157)

It is evident that the confidence interval is smaller, as the confidence level is reduced.

<em>This means that by reducing the confidence level for same sample size, the confidence interval is reduced.</em>

Part c

As from given data

  • Percentage of co-workers already received flu vaccine p=0.36,
  • n=200

The confidence interval is given as

CI=\hat{p} \pm z_{\alpha}\sqrt{\frac{p(1-p)}{n}}

Here

  • z is given for 98% confidence level as 2.33

By substituting values in the equation

CI=\hat{p} \pm z_{\alpha}\sqrt{\frac{p(1-p)}{n}}\\CI=0.36 \pm 2.33\sqrt{\frac{0.36(1-0.36)}{200}}\\CI=0.36 \pm 0.07899\\CI=(0.2810,0.4389)

It is evident that the confidence interval is greater, as the confidence level is increased.

<em>This means that by increasing the confidence level for same sample size, the confidence interval is increased.</em>

You might be interested in
The zero coupon bonds of JK Industries have a market price of $211.16, a face value of $1,000, and a yield to maturity of 7.39 p
Nutka1998 [239]

Answer:

It will take about 22 years until the bonds mature.

Explanation:

This can calculated as follows:

BP = FV/(1 + r)^n ..................................... (1)

Where;

BP = Bond price = $211.16

FV = Face value of $1,000

r = Yield to maturity = 7.39%, or 0.0739

n = number of years for the bond to mature = ?

Substituting the values into equation (1) we have:

211.16 = 1,000/(1 + 0.0739)^n

211.16 [(1.0739)^n] = 1,000

(1.0739)^n = 1,000/211.16

(1.0739)^n = 4.73574540632696

Log-linearizing the above, we have:

nln (1.0739) = ln(4.73574540632696)

n = ln(4.73574540632696)/ln (1.0739)

  = 1.55513913902672/0.0712968818820338  

  = 21.8121620185272

n = 22 years approximately

Therefore, it will take about 22 years until the bonds mature.

4 0
3 years ago
During the norming stage of team development, team members: try to establish a favorable role for themselves on the team. meet e
ExtremeBDS [4]
During the norming stage of team development, team members: begin to settle into their roles as team members.
6 0
3 years ago
Xavier and Yolonda have original investments of $100,000 and $50,000 respectively in a partnership. The articles of partnership
sveticcg [70]

Answer:

Total of Xavier's share = $49750

Explanation:

The allocation of net income to both Xavier and Yolonda will be as follows,

Net Income                              90000

<u>Interest on Capital:</u>

Xavier(0.15 * 100000)      15000  

Yolonda(0.15 * 50000)    <u>  7500</u>   <u> (22500) </u>

                                              67500

<u>Salary:</u>  

Xavier                           22000  

Yolonda                           <u>20000</u>      (<u>42000)</u>

                                               25500

<u>Share of remaining profit:</u>  

Xavier                             12750  

Yolonda                             <u>12750</u>        <u>25500 </u>

<u />

Total of Xavier's share = 15000 + 22000 + 12750  = $49750

4 0
3 years ago
Treasury bills are paying a 4% rate of return. A risk-averse investor with a risk aversion of A = 3 should invest entirely in a
Tomtit [17]

Answer:

Answer is 12.64%. Therefore,

Treasury bills are paying a 4% rate of return. A risk-averse investor with a risk aversion of A = 3 should invest entirely in a risky portfolio with a standard deviation of 24% only if the risky portfolio's expected return is at least 12.64%.

Refer below for the explanation.

Explanation:

E - 4%= 0.5(3)(24%)2

E=12.64%

7 0
3 years ago
Read 2 more answers
Explain what a credit score is and what it tells you about the consumer. What are some ways you can maintain a proper credit sco
Dovator [93]
A credit score is a score that measures how likely you are to pay back a loan. If the score Is good that means they paid their loans on time. if the score is bad that means they aren't likely to pay any payments they are given through a loan. You can maintain a proper score by paying bills on time, when taking out loans pay the payments on time. and when you loan a car Pay. The. Payments.
6 0
3 years ago
Read 2 more answers
Other questions:
  • What is meant by a viable business idea?
    12·1 answer
  • If businesses use the internet to find less expensive resources, what will be the impact on productivity
    6·2 answers
  • Suppose Grady starts out with a full tank of gas in his car, and drives 540 miles home from college for spring break. Once he ge
    11·1 answer
  • A monopolistic seller of sports cars has traced out the following demand curve: 10 customers have willingness to pay (WTP) of $1
    5·1 answer
  • A contractor who agrees to undertake work without being under the direct control or direction of another and is personally respo
    10·1 answer
  • Krisp Systems decides to move production to a developing country where they are free to pump pollutants into the atmosphere with
    12·1 answer
  • Sales and excise taxes are levied on retailers, but retailers add these taxes to the prices of their products. this illustrates
    8·1 answer
  • Type the correct answer in the box. Spell all words correctly
    10·2 answers
  • The Up and Coming Corporation's common stock has a beta of 0.9. If the risk-free rate is 4 percent and the expected return on th
    9·1 answer
  • Alex has accepted an IT position at a new company, and will be leaving her current job in the IT department of a large company.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!