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elena-s [515]
2 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]2 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.

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SSA

Step-by-step explanation:

4 0
3 years ago
Julio bought tables and chairs for his restaurant. He bought 16 total items and spent $1800. Each table cost $150 and each chair
uysha [10]

Answer:

He bought 6 chairs and 10 tables.

Step-by-step explanation:

x+y = 16

he spent = $1800

1 chair = $50

y chairs = $50y

1 table = $150

x chairs = $150x

so, 150x+50y = 1800

we got two equations :

x+ y = 16

150x+50y = 1800

Using. substitution method,

x+y = 16

so, x = 16-y

Now

150x+50y =1800

or, 150(16-y) + 50y = 1800

or, 2400-150y+50y = 1800

or, 2400-1800 = 150y-50y

or, 600=100y

so, y = 6

now,

x+y = 16

or, x + 6 = 16

so, x = 10

4 0
2 years ago
Meeta buys a ticket for the movie and a popcorn, which costs $6. She spends $16.50 in all. How much was the movie ticket?
Sav [38]

Answer:

10.50

Step-by-step explanation:

16.50-6

6 0
2 years ago
(3/5)^2+4X3-2 what is the value of the expression
Sliva [168]

Answer:

10.36

Step-by-step explanation:

So your solution would be:

(\frac{3}{5})^{2} + 4 \times 3 - 2

=(\frac{3}{5})^{2} + 4 \times 3 - 2

=\dfrac{3^{2}}{5^{2}} + 4 \times 3 - 2

=\dfrac{9}{25} + 4 \times 3 - 2

=0.36 + 4 \times 3 - 2

=0.36 + 12 - 2

=12.36 - 2

=10.36

Just try to remember PEMDAS.

Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction.

This is the order we follow when going about expressions with many operations.

Let's start with the parenthesis part. Notice that there is an exponent beside the parenthesis enclosing the fraction. Here we use the quotient to a power rule. We distribute the exponent to the numerator and the denominator.

=(\frac{3}{5})^{2} + 4 \times 3 - 2\\

=\dfrac{3^{2}}{5^{2}} + 4 \times 3 - 2

=\dfrac{9}{25} + 4 \times 3 - 2

Now that we got the parenthesis and exponent out of the way, let's move on to the next. Multiplication/Division. Whichever comes first, you do it first.

We have a fraction so we do that first. Then we do the multiplication after.

=0.36 + 4 \times 3 - 2

=0.36 + 12 - 2

Next we do the addition/subtraction. Again, whichever comes first.

=12.36 - 2

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7 0
3 years ago
Dimensions of a Box A large plywood box has a volume of . Its length is ft greater than its height, and its width is ft less tha
cupoosta [38]

Answer:

Few things are missing, they are volume of the box is 180 feet cube. Length is 9 feet greater than its height, and weight is 4 feet less than its height.

Step-by-step explanation:

Given, the volume of the box, V = 180 feet cube

Let the height of the box, h = x feet

Therefore, length is, l = ( 9+x ) feet

And width is, b = ( x-4) feet

so volume of the box is

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Factorizing we get

(x+5)(x-6)(x+6)=0

Therefore,

x = -5, -6, 6

Now since the height of the box cannot be negative, so taking the positive value of x, we get

Height of the box, h = x = 6 feet

Length , l = ( 9+x ) = 9+6 = 15 feet

Width , b = ( x-4) = 6-4 = 2 feet

8 0
3 years ago
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