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
elena-s [515]
3 years ago
10

In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hir

ed by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008
a. Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of .
b. Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
c. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of .
d. Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?
Mathematics
1 answer:
Ede4ka [16]3 years ago
6 0

Answer:

Explained below.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 \mu_{\hat p}= p

The standard deviation of this sampling distribution of sample proportion is:

 \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}

(a)

The sample selected is of size <em>n</em> = 450 > 30.

Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.

The mean and standard deviation are:

\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{450}}=0.0204

So, the sampling distribution of sample proportion is \hat p\sim N(0.75,0.0204^{2}).

(b)

Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:

P(p-0.04

                                          =P(-1.96

Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.95.

(c)

The sample selected is of size <em>n</em> = 200 > 30.

Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.

The mean and standard deviation are:

\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{200}}=0.0306

So, the sampling distribution of sample proportion is \hat p\sim N(0.75,0.0306^{2}).

(d)

Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:

P(p-0.04

                                          =P(-1.31

Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.81.

(e)

The probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 450 is 0.95.

And the probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 200 is 0.81.

So, there is a gain in precision on increasing the sample size.

You might be interested in
A number has the digit 3 in the once place and the digit 4 in the tens place.which of these is another way to write this number?
Anarel [89]
The best way will be 40+3
3 0
3 years ago
Read 2 more answers
The question is in the picture
Blizzard [7]
I think is that one that say <-5,-3> yeah because 3×5=15 you have to choose what other number × 3 that equal to that following answer.
3 0
3 years ago
What is 3/20 of 75???????
mars1129 [50]
The answer to your question is 11.25
4 0
3 years ago
Geometry!!Find the area of the rhombus!!
mars1129 [50]

The area of a rhombus is half of the product of the lengths of the diagonals.

area = (7.5 yd + 7.5 yd)(13 yd + 13 yd)/2

area = (15 yd)(26 yd)/2

area = 390 yd^2/2

area = 195 yd^2

Answer: 195

7 0
3 years ago
What equation represents a parabola with a focus of (0,4) and a directrix of y=2
scZoUnD [109]
We know that

Any point <span>(x,y)</span> on the parabola is equidistant from the focus and the directrix

Therefore,

focus (0,4) and directrix of y=2

<span>√[<span>(x−0)</span></span>²+(y−4)²]=y−(2)

<span>√[x</span>²+(y-4)²]=y-2

x²+(y-4)²=(y-2)²

x²+y²-8y+16=y²-4y+4

x²=4y-12-----> 4y=x²+12----->y= (x²/4)+3


the answer is

y= (x²/4)+3


7 0
3 years ago
Other questions:
  • Jackson says he has an odd number of model cars. He has 6 cars on one shelf and 8 cars on another shelf. Is Jackson correct? Exp
    15·1 answer
  • The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as
    12·1 answer
  • in a bag of red and yellow cookies the ratio of red cookies to Yellow cookies is 4 :5 if the bag contains 80 yellow cookies how
    13·1 answer
  • Which statements are true regarding the data displayed in the box plots? Check all that apply
    12·2 answers
  • What is the first step to solve 6x-2=-4x+2
    14·1 answer
  • What are the solutions of −1 ≤ x − 3 &lt; 4? Graph the solution. giving alot of points and ill give branliest
    8·1 answer
  • A $100 pair of headphones is marked down by 10% and you also have a 20% off coupon. What is the final price, before tax?
    15·1 answer
  • Whats the volume the triangular prism?​
    10·1 answer
  • In 2.2, recall that on an open interval, the end points are not included in the interval. For example, the open interval (2, 4)
    6·1 answer
  • Simplify the expression.<br> 2.4 - 4.3n - 3n + 6
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!