MAT 130: Beginning Statistics

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Student Name

Allied American University

Author Note

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

PART I: SHORT RESPONSE

Directions: Please answer each of the following questions thoroughly.

1. What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

2. What is the difference between a standard normal distribution and a nonstandard normal distribution?

3. Find the indicated values for the following problems:

a. z0.05

b. z0.01

c. z0.10

d. z0.02

4. Based on data from the National Health Survey, men’s heights are normally distributed with mean 69.0 in. and standard deviation 2.8 in, whereas women’s heights are normally distributed with mean 63.6 in. and standard deviation 2.5 in. The Gulfstream 100 is an executive jet that seats six, and it has a doorway height of 51.6 in. Use this information to answer the following problems:

a. What percentage of adult men can fit through the door without bending?

b. What percentage of adult women can fit through the door without bending?

c. Does the door design with a height of 51.6 in. appear to be adequate? Why didn’t the engineers design a larger door?

d. What doorway height would allow 60% of men to fit without bending?

5. What is the standard error of the mean?

6. Assume that SAT scores are normally distributed with mean μ = 1518 and standard deviation σ = 325. Use the Central Limit Theorem to answer the following:

a. If 1 SAT score is randomly selected, find the probability that it is greater than 1600.

b. If 64 SAT scores are randomly selected, find the probability that they have a mean greater than 1600.

7. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.

a. n = 500, x = 220, 99% confidence

b. 90% confidence; the sample size is 1780, of which 35% are successes

8. Use the given sample data and confidence level to construct the confidence interval estimate of the population proportion p for each problem.

a. n = 2000, x = 400, 95% confidence

b. n = 5200, x = 4821, 99% confidence

9. A design engineer for the Ford Motor Company must estimate the mean leg length of all adults. She obtains a list of the 1275 employees at her facility, then obtains a simple random sample of 50 employees. If she uses this sample to construct a 95% confidence interval to estimate the mean leg length for the population of all adults, will her estimate be good? Why or why not?

10. A simple random sample of 40 salaries of NCAA football coaches has a mean of $415,953 and a standard deviation of $463,364.

a. Find the best point estimate of the mean salary of all NCAA football coaches.

b. Construct a 95% confidence interval estimate of the mean salary of an NCAA football coach.

c. Does the confidence interval contain the actual population mean of $474,477?

11. Use the given confidence level and sample data below to find (a) the margin of error and (b) the confidence interval for the population mean. Assume that the sample is a simple random sample and the population has a normal distribution. 99% confidence; n = 7, = 0.12 , s = 0.04

12. What is an unbiased estimator? Is the sample variance an unbiased estimator of the population variance? Is the sample standard deviation an unbiased estimator of the population standard deviation?

13. Use the given confidence level and sample data to find a confidence interval for the population standard deviation. In each case, assume that a simple random sample has been selected from a population that has a normal distribution. 95% confidence; n = 25, = 81.0, s = 2.3

14. Twelve different video games showing substance use were observed and the duration times of game play (in seconds) are listed below (based on data from “Content and Ratings of Teen-Rated Video Games,” by Haninger and Thompson, Journal of the American Medical Association, Vol. 291, No. 7). The design of the study justifies the assumption that the sample can be treated as a simple random sample. 4049 3884 3859 4027 4318 4813 4657 4033 5004 4823 4334 4317

a. Use the sample data to construct a 95% confidence interval estimate of μ, the mean duration of game play.

b. Use the sample data to construct a 99% confidence interval estimate of σ, the standard deviation of the duration times of game play.

PART II: PROJECT

For this Module 4 Homework Assignment, please submit your response to the following:

Document your progress. Who did you interview? How many people did you interview? If you collected data, please submit it below. If not, please explain what you did to contribute to this assignment this past week.

Directions: This assignment is a course-long project whereby you will work on the project in each module. You will turn in your completed project at the end of Module 8.

Create a survey question to ask others. The following are examples or some survey questions:

1. Choose a random number between 1 and 10 inclusive.

2. What month of the year does your birthday fall on? Write the numeric value from 1 to 12.

3. How many keys are in your possession at this time?

4. How many siblings do you have?

In Module 1, you will submit your survey question to your instructor for approval. Once you are notified of its approval, you may begin conducting a survey using your question.

You will need at least 25 participants and will need to keep the following record for each person:

a. Gender

b. Age

c. Date surveyed

d. Survey response

Please also keep a count, if any, non-willing participants. For example, if you chose the first survey question, then you might have the following records:

In the Module 8 Homework Assignment, you will be asked to analyze your survey results, so please be sure to begin conducting your survey as soon as your question is approved. Try getting 5 participants a week to satisfy the required number of participants.