Stats Preparation Assignment (75 points)
Note: you may discuss with your peers, refer to books and online resources, and the review materials I posted on BB. However, you should not COPY and PASTE the answers. Please try best to digest the materials through examples. Please cite the book or website you use to come up with the answers for Part I.
A book (Business Statistics by Robert A. Donnelly, Jr.) will be reserved in the library on the west campus to help you review the materials.
Part I: Essay Questions (40 points)
1. What is Z score? How to obtain Z score? Why do we want to have Z score sometimes?
Z score is
2. Briefly state what Central Limit Theorem is and its applications (you may refer to the text book page 321).
3. What is standard error of the mean? How to obtain it? How does it relate to Central Limit Theorem?
4. What is a discrete probability distribution? What’s a continuous probability distribution?
5. What is descriptive statistics? What is inferential statistics? What’s the difference?
6. What is sample statistics? What is a population parameter? What is sampling error? How does increasing sample size affect sampling error?
7. What is confidence interval of a mean or a proportion? What’s margin of error? How to obtain both?
8. What’s null hypothesis? What’s alternative hypothesis? What is p value?
Part II: Exercises (35 points) (please spell the steps involved in calculations; you will get zero points with no steps shown even if your answer is correct)
a. The following table shows the frequency distribution for the mileage on a sample of Avis rental cars:
5,000 to under 6,000 16
6,000 to under 7,000 11
7,000 to under 8,000 24
8,000 to under 9,000 10
9,000 to under 10,000 15
10,000 to under 11,000 9
a) Calculate the approximate average mileage per car for the sample.
b) Calculate the approximate variance and standard deviation for the sample.
b. A random variable follows the normal probability distribution with a mean of 80 and a standard deviation of 20. What is the probability that a randomly selected value from this population
a) is less than 90?
b) is less than 65?
c. According to Smith Travel Research, the average hotel price in the United States in 2009 was $97.68. Assume the population standard deviation is $18.00 and that a random sample of 35 hotels was selected.
Calculate the standard error of the mean.
b) What is the probability that the sample mean will be less than $100
c) What is the probability that the sample mean will be more than $102
d) What is the probability that the sample mean will be between $96 and $98?
d. With a capacity of 6,300 people, Royal Caribbean’s Oasis of the Seas is the world’s largest cruise ship. The average beer consumption over 15 randomly selected seven-day cruises on the ship was 81,740 bottles with a sample standard deviation of 4,590 bottles. Royal Caribbean would like to estimate the average beer consumption to plan its beer inventory levels on future cruises. (The ship certainly doesn’t want to run out of beer in the middle of the ocean!)
Construct a 95% confidence interval to estimate the average beer consumption per cruise.
b) What assumptions need to be made about this population?
e. The IRS reported that 62% of individual tax returns were filed electronically in 2008. A random sample of 225 tax returns from 2010 was selected. From this sample, 163 were filed electronically.
a) Construct a 95% confidence interval to estimate the actual proportion of taxpayers who filed electronically in 2010.
b) What is the margin of error for this sample?
c) Is there any evidence that this proportion has changed since 2008 based on this sample?