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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.

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Tobin is solving the equation 3(x - 1.25) = 11.25. His work is shown below.
castortr0y [4]

Answer: In the last steps, instead of multiply each side by 3, he has to divide each side by 3.

Step-by-step explanation:

Hi, Tobin makes the mistake in the last steps.

3(x-1.25) = 11.25  

3x-3.75= 11.25  

3x-3.75+3.75= 11.25+3.75  

3x = 15

Until this step is the work ok.

Now, instead of multiply each side by 3, he has to divide each side by 3:

So:

3x /3 = 15/3

x = 5

Feel free to ask for more if needed or if you did not understand something.

6 0
3 years ago
I NEED HELP please!!
swat32

9514 1404 393

Answer:

  (c)  11

Step-by-step explanation:

As x goes up by 1, f(x) goes up by 2. The next line of the chart would be ...

  x = 4+1 = 5; f(x) = 9+2 = 11

The appropriate choice is f(5) = 11.

5 0
3 years ago
A baby who was 18 inches at birth is now 24 inches by what percentage did the babys height increase
Kazeer [188]

Answer:

≈33.3%

Step-by-step explanation:

First we find the difference of the heights to see what the growth was

24-18 = 6

Then we find what percent 6 is of 18 to see what percentage growth occured

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8 0
2 years ago
Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the
Annette [7]

Answer:

  • (a) 3 inches

  • (b)  Her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches because the dimensions are not proportional to the scale.

Explanation:

(a) What is the length of the garden in her model? Show your work, including your proportion

<u>1. Scale</u>:

  • model length / real length = 1 inch / 2 feet

<u>2. Proportion</u>:

Naming x the model length:

  • 1 inch / 2 feet = x / 6 feet

Cross multiply:

  • 1 inch × 6 feet = 2 feet × x

Divide both sides by x:

  • x = 1 inch × 6 feet / 2 feet = 3 inch.

Answer: 3 inches

(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?​

Both the width and the length must use the same scale, thus the corresponding sides of the scale model and the drawing must be proportional.

In the model the ratio of the length to the width is 3 inch / 5 inch

In the paper the ratio of the length to the width is 8.5 inch / 7 inch

Hence, you can see that in the model the length (mumerator of the fraction) is less than the width (denominator) while in the paper it is the opposite. Bieng the two ratios different, they are not proportional, and you conclude that her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches.

8 0
3 years ago
WRITE DOWN THE FALUE OF 7
Maru [420]

Answer:

(I need to know where the seven is located/placed.) Please give a clear answer or attach a photo next time so everybody who sees your question will understand.

Step-by-step explanation:

Comparing the numbers 700, 70, and 7; the digit "7" has a different value depending on its place within the number.

7 - ones place

70 - tens place

700 - hundreds place

The place value of the 7 determines the value it holds for the number. As the place moves to the left, the value of the number becomes greater by 10 times

8 0
3 years ago
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