CHAPTER 7 PROJECT

SCENARIO 1: THE BASICS

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MOVING ONTO THE FORMULAS

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QUESTIONS

• 1. What is the best point estimate for population proportion? The best way to estimate a population proportion with a single value is by using the sample proportion P hat. since p hat is a single value it is a point estimate.

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• 2. What is the best point estimate for population mean? The sample mean x bar is the best point estimate of the population mean.

QUESTIONS

• 3. What is the best point estimate for population variance? The sample variance S squared is the best point estimate of the population mean.

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• 4. Why should we NOT use sample standard deviation as a point estimate for population standard deviation, even though it is? It introduces a source of unreliability especially with small samples. Instead we use critical values T a/2 that are larger than the critical values of z a/2 from the normal distribution. The critical value of ta/2 can be found by using a calculator or table a-3 but first we have to identify the number of degrees of freedom.

SCENARIO 2: SKITTLES

The folks at the Mars Candy company claim that there is an even chance of getting any color of Skittles candy in a package. We want to test this. Let’s start with the company’s assumption that for each color, red, green, orange, yellow, and purple, there is a 20% chance for each

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I chose the green skittles to construct the 95% confidence interval.
.12843

P hat=.2
N=120

We are 95% confident that the interval from.12843 and .27157 contains the true value of the population proportion p. If we were to select many different samples of 120 and construct the corresponding confidence intervals, 95% of them would contain the value of the population proportion

QUESTIONS

• 1. A factory has learned that it produces sheets of aluminum that have a mean length of 27cm with a standard deviation of 0.04cm. What is the probability that we would randomly select a sheet that has a length greater than 27.1cm?
• Normalcdf (27.1,1E99,27,0.04) =0.0062

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• 2. Standard Components produces resistors with a mean rating of 22.75 ohms and a standard deviation of 0.05 ohms. What is the probability that a randomly selected resistor will have an ohm rating less than 22 ohms?
• Normal cdf(-1E99, 22, 22.75, 0.05) = 0

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• 3. General Electric’s home meters are rated to handle at most 150 A of current. If the electrical usages of the mean home in Southern California is 135 A with a standard deviation of 5.9 A, what is the probability that a randomly selected meter will fail at any given point?
• Normal cdf(-1E99, 150,135,5.9)= 0.9944

Scenario 3: Using Raw Data

The corporate line at Nissan is that their electric vehicle, the Leaf, has a battery that outperforms the average all-electric car. If the average all electric car has a capacity that exceeds 75% after 5 years, are the people at Nissan being honest?

I constructed a 95% confidence interval for the mean using the data in the "remaining capacity 5 years" column.
70.158

QUESTIONS

• 1. Comment, based on your findings, about the company’s claim that their vehicle is “better than average.” Be sure to include your interpretation of your confidence interval.
• I found that the vehicle's 5 year capacity was slightly below the average.

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• We are 95% confident that the interval from 70.158 to 73.917contains the true value if mu. If we were to select many different samples of the same size and construct the corresponding conference intervals, 95% of them would have the true value of mu.

QURSTIONS

• 2. Would you recommend this car based on your findings? Why or why not?
• I would not as it is slightly below average. The average electric car has a capacity that exceeds 75% after 5 years but there is a 95% chance that the Leaf by Nissan will have a capacity between 70.158 to 73.917. Those findings weren't exactly horrible but they did not impress me after hearing Nissan's claim that it better than average.

SCENARIO 4: QUESTION EVERYTHING

I asked my friends who were avid listeners of music of the lo-fi indie genre if they preferred Ariel Marcus Rosenberg's musical project of Ariel Pink or Ariel Pink's Haunted Graffiti. These were the results ...

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QUESTIONS

• 1. If you wish to create a 99% confidence interval for your population proportion, what is the best point estimate for your population proportion?
• The sample proportion P hat is the best point Estimate of the population proportion
• P hat= .55

QUESTIONS

• 2. Create the confidence interval and provide the correct interpretation. Be sure to identify which of your two answers is your “success” answer and which is your “failure” answer.
• The "success" is Ariel Pink and the "failure" is Ariel Pink's Haunted Graffiti
• 99% confidence interval for Ariel pink: 0.26346

• P hat= .55 n=20

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• We are 99% confident that the interval from 0.26346 to 0.83654 contains the true value if p hat. If we were to select many different samples of the same size and construct the corresponding conference intervals, 99% of them would have the true value of p hat.

Conclusion
I felt that this project helped me get a better understanding of how to construct a confidence interval for population proportion and mean. I felt that this project could have included some problems that focused on variance and degrees of freedom. This project was also a good reminder on how to use the normal cdf function on a calculator.