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# \$30.00Normal Distributions and Confidence Intervals

• From Mathematics: Statistics
• Closed, but you can still post tutorials
• Due on Apr. 09, 2010
• Asked on Apr 05, 2010 at 9:31:19PM

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Tutorials Posted: 38,
Earned: \$285.00

Q:
 Part 1:  Normal Distributions and Birth Weights in America

You should carefully work through the examples provided inside the Normal Ex worksheet in our Lab 6 Excel file (linked above or here ).  The examples shown are similar to your assignment.

Use Excel to answer the quesitons presented in the case study Birth Weights in America, Birth Weights .  Essentially, you'll use Excel functions to answer the questoins that are described in the problem.  Remember that each "gestation pierod" is its own normal distribution with its own mean and standard deviation.

 Part 2:  Central Limit Theorem and Age Distribution in the United States

Use Excel to answer the questions presented in the Age Distribution in the United States Technology problem, Age Distribution .  Be sure to use the Age Dist worksheet in our Lab 6 Excel file (linked above or here ) to help answer the questions.  Some of the required work is already started in that worksheet.

Place your answers inside the Week 6 Lab Template.  Be sure to follow the directions given in the file.

 Part 3:  Finding z- and t-scores for Confidence Intervals

Finding appropriate z- and t-scores is important when constructing confidence intervals.  Confidence intervals allow one to estimate important population parameters such as population mean, population proportion, population standard deviation, etc.  We will also study how confidence intervals will let one determine how large of a sample is required in order to get within a desired error range.  Thus, confidence intervals offer important real-world applications.  In Part 4 of this lab (described below) you will use a population mean confidence interval to determine if the local economy is sufficient to handle a new candy-making business.

Part 3, however, focuses on finding the correct z- and t-scores for a given confidence level.  You should carefully follow the examples located inside the Conf Intervals worksheet in our Lab 6 Excel fileThen, answer the following questions.  Note that these questions are also inside the worksheet.

1.  Using Excel, find the z-score that corresponds to the following Confidence Levels:

a.  80%
b.  85%
c.  92%
d.  97%

2.  Using Excel, find the t-score that corresponds to the following Confidence Levels and Sample Sizes:

a.  95% with n = 25
b.  96% with n = 15
c.  97% with n = 21
d.  91% with n = 10

Place your answers inside the Week 6 Lab Template.  Be sure to follow the directions given in the file.

 Part 4:  Bob's Candies  (Using Confidence Intervals to decide a course of action)

This part of the lab asks you to use your work from previous labs, as well as your knowledge of confidnece intervals to decide whether or not the local economy is strong enough to support a new candy-making business.  Bob enjoys making candy and some friends have encouraged him to open a candy-making business.  To see if the local citizens buy enough candy, Bob gathers a sample of how much money they spend annually on the type of candy Bob will make.  You will help Bob analyze this data to see if they spend more than the national average.  If so, Bob thinks there will be enough demand to support his new candy-making business.

The dollars spent per person is given in the Candy Business worksheet in our Lab 6 Excel file.

After you analyze the data, answer the following questions.

1.  Find the sample mean and sample standard deviation of the amount citizens spend per year.

2.  When finding a confidence interval for the true mean spent of ALL citizens, should we use a z-score or a t-score?  Why?

3.  Find the z/t-values (as appropriate) for a 95% confidence interval and a 92% confidence interval.

4.  Find a 95% and a 92% confidence interval for the true mean amount that citizens spend per year.

5.  What do you think the lowest possible mean amount spent per year is?  Why?

6.  Do you think Bob has a good customer base for his new business?  Explain.